The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A178561

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

A178561

Primes q from A178548.
(history; published version)

#10 by Susanna Cuyler at Sun Feb 17 08:53:17 EST 2019

STATUS

reviewed

approved

#9 by Michel Marcus at Sun Feb 17 01:14:40 EST 2019

STATUS

proposed

reviewed

#8 by G. C. Greubel at Sat Feb 16 22:43:54 EST 2019

STATUS

editing

proposed

#7 by G. C. Greubel at Sat Feb 16 22:42:26 EST 2019

LINKS

G. C. Greubel, <a href="/A178561/a178561.txt">List of triples (prime(n+2), p=A178548(n), q=A178561(n)) for n=0..100</a>

#6 by G. C. Greubel at Sat Feb 16 22:33:48 EST 2019

DATA

31, 11, 313, 23, 163, 53, 157, 43, 41, 71, 103, 137, 61, 127, 193, 227, 113, 109, 107, 101, 277, 127, 101, 223, 113, 181, 251, 571, 233, 409, 151, 257, 211, 317, 491, 557, 661, 733, 367, 433, 359, 313, 491, 271, 233, 509, 281, 241, 311, 271, 373, 1163, 613, 571

LINKS

G. C. Greubel, <a href="/A178561/b178561.txt">Table of n, a(n) for n = 1..10000</a>

EXAMPLE

2*13 + prime(3) = 26 + 5 = 31 = prime(11), soddigsum(13)=soddigsum(31)=4

2*2 + prime(4) = 4 + 7 = 11 = prime(5), soddigsum(2)=soddigsum(11)=2

2*151 + prime(5) = 302 + 11 = 313 = prime(65), soddigsum(151)=soddigsum(313)=7

2*5 + prime(6) = 10 + 13 = 23 = prime(9), soddigsum(5)=soddigsum(23)=5, etc.

PROG

(PARI) a(n) = {my(p=2, q=prime(n+2)+2*p); while ((!isprime(q) || (sumdigits(p) != sumdigits(q))), p = nextprime(p+1); q = prime(n+2) + 2*p); q; }

vector(70, n, a(n)) \\ G. C. Greubel and Michel Marcus, Feb 26 2019

EXTENSIONS

a(37) corrected by G. C. Greubel, Feb 16 2019

STATUS

approved

editing

#5 by Jon E. Schoenfield at Sun Mar 15 20:56:25 EDT 2015

STATUS

editing

approved

#4 by Jon E. Schoenfield at Sun Mar 15 20:56:22 EDT 2015

COMMENTS

See comments in A178548.

EXAMPLE

From Robert G. Wilson v, Aug 23 2010: (Start)

(End)

MATHEMATICA

f[n_] := Block[{p = 2}, While[q = 2 p + Prime[n + 2]; !PrimeQ@q || Plus @@ IntegerDigits@p != Plus @@ IntegerDigits@q, p = NextPrime@p]; q]; Array[f, 53] (* _Robert G. Wilson v_, Aug 23 2010 *)

CROSSREFS

Cf. A000040, A001358, A178548.

EXTENSIONS

I removed all of the All comments and added several examples and a Mathematica coding _removed by _Robert G. Wilson v_, Aug 23 2010

STATUS

approved

editing

#3 by Russ Cox at Fri Mar 30 17:31:29 EDT 2012

EXTENSIONS

I removed all of the comments and added several examples and a Mathematica coding _Robert G. Wilson v (rgwv(AT)rgwv.com), _, Aug 23 2010

Discussion

Fri Mar 30

17:31

OEIS Server: https://oeis.org/edit/global/156

#2 by N. J. A. Sloane at Sun Sep 12 03:00:00 EDT 2010

COMMENTS

2*13+prime(3)=26+5=31=prime(11), sod(13)=sod(31)=4

2*2+prime(4)=4+7=11=prime(5), sod(2)=sod(11)=2

2*151+prime(5)=302+11=313=prime(65), sod(151)=sod(313)=7

2*5+prime(6)=10+13=23=prime(9), sod(5)=sod(23)=5

2*73+prime(7)=146+17=163=prime(38), sod(73)=sod(163)=10

2*17+prime(8)=34+19=53=prime(16), sod(17)=sod(53)=8

2*67+prime(9)=134+23=157=prime(37), sod(67)=sod(157)=13

2*7+prime(10)=14+29=43=prime(14), sod(7)=sod(43)=7

2*5+prime(11)=10+31=41=prime(13), sod(5)=sod(41)=5

2*17+prime(12)=34+37=71=prime(20), sod(17)=sod(71)=8

2*31+prime(13)=62+41=103=prime(27), sod(31)=sod(103)=4

2*47+prime(14)=94+43=137=prime(33), sod(47)=sod(137)=11

2*7+prime(15)=14+47=61=prime(18), sod(7)=sod(61)=7

2*37+prime(16)=74+53=127=prime(31), sod(37)=sod(127)=10

2*67+prime(17)=134+59=193=prime(44), sod(57)=sod(193)=13

2*83+prime(18)=166+61=227=prime(49), sod(83)=sod(227)=11

2*23+prime(19)=46+67=113=prime(30), sod(23)=sod(113)=5

2*19+prime(20)=38+71=109=prime(29), sod(19)=sod(109)=10

2*17+prime(21)=34+73=107=prime(28), sod(17)=sod(107)=8

2*11+prime(22)=22+79=101=prime(26), sod(11)=sod(101)=2

2*97+prime(23)=194+83=277=prime(59), sod(97)=sod(277)=16

2*19+prime(24)=38+89=127=prime(31), sod(19)=sod(127)=10

2*2+prime(25)=4+97=101=prime(26), sod(2)=sod(101)=2

2*61+prime(26)=122+101=223=prime(48), sod(61)=sod(223)=7

2*5+prime(27)=10+103=113=prime(30), sod(5)=sod(113)=5

2*37+prime(28)=74+107=181=prime(42), sod(37)=sod(181)=10

2*71+prime(29)=142+109=251=prime(54), sod(71)=sod(251)=8

2*229+prime(30)=458+113=571=prime(105), sod(229)=sod(571)=13

2*53+prime(31)=106+127=233=prime(51), sod(53)=sod(233)=8

2*139+prime(32)=278+131=409=prime(80), sod(139)=sod(409)=13

2*7+prime(33)=14+137=151=prime(36), sod(7)=sod(151)=7

2*59+prime(34)=118+139=257=prime(55), sod(59)=sod(257)=14

2*31+prime(35)=62+149=211=prime(47), sod(31)=sod(211)=4

2*83+prime(36)=166+151=317=prime(66), sod(83)=sod(317)=11

2*167+prime(37)=334+157=491=prime(94), sod(167)=sod(491)=14

2*197+prime(38)=394+163=557=prime(102), sod(197)=sod(557)=17

2*247+prime(39)=494+167=661=prime(121), sod(247)=sod(661)=13

2*97+prime(40)=194+173=367=prime(73), sod(97)=sod(367)=16

2*127+prime(41)=254+179=433=prime(84), sod(127)=sod(433)=10

2*89+prime(42)=178+181=359=prime(77), sod(89)=sod(359)=17

2*61+prime(43)=122+191=313=prime(65), sod(61)=sod(313)=7

2*149+prime(44)=298+193=491=prime(94), sod(149)=sod(491)=14

2*37+prime(45)=74+197=271=prime(58), sod(37)=sod(271)=10

2*17+prime(46)=34+199=233=prime(51), sod(17)=sod(233)=8

2*149+prime(47)=298+211=509=prime(97), sod(149)=sod(509)=14

2*29+prime(48)=58+223=281=prime(60), sod(29)=sod(281)=11

2*7+prime(49)=14+227=241=prime(53), sod(7)=sod(241)=7

2*41+prime(50)=82+229=311=prime(64), sod(41)=sod(311)=5

2*19+prime(51)=38+233=271=prime(58), sod(19)=sod(271)=10

2*67+prime(52)=134+239=373=prime(74), sod(67)=sod(373)=13

2*461+prime(53)=922+241=1163=prime(192), sod(461)=sod(1163)=11

2*181+prime(54)=362+251=613=prime(112), sod(181)=sod(613)=10

2*157+prime(55)=314+257=571=prime(105), sod(157)=sod(571)=13

2*97+prime(56)=394+263=457=prime(88), sod(97)=sod(457)=16

2*19+prime(57)=38+269=307=prime(63), sod(19)=sod(307)=10

2*89+prime(58)=178+271=449=prime(87), sod(89)=sod(449)=17

2*83+prime(59)=166+277=443=prime(86), sod(83)=sod(443)=11

2*79+prime(60)=158+281=439=prime(85), sod(79)=sod(439)=16

2*167+prime(61)=354+283=617=prime(113), sod(167)=sod(617)=14

2*139+prime(62)=278+293=571=prime(105), sod(139)=sod(571)=13

2*107+prime(63)=214+307=521=prime(98), sod(107)=sod(521)=8

2*453+prime(64)=906+311=1217=prime(199), sod(453)=sod(1217)=13

2*353+prime(65)=706+313=1019=prime(171), sod(353)=sod(1019)=11

2*7+prime(66)=14+317=331=prime(67), sod(7)=sod(331)=7

2*443+prime(67)=886+331=1217=prime(199), sod(443)=sod(1217)=11

2*491+prime(68)=982+337=1319=prime(215), sod(491)=sod(1319)=14

2*157+prime(69)=314+347=661=prime(121), sod(157)=sod(661)=13

2*47+prime(70)=94+349=443=prime(86), sod(47)=sod(443)=11

2*97+prime(71)=194+353=547=prime(101), sod(97)=sod(547)=16

2*37+prime(72)=74+359=433=prime(84), sod(37)=sod(433)=10

EXAMPLE

i=1: 2*13+prime(3)=26+5=31=prime(11), sod(13)=sod(31)=4, 31 is first term

i=2: 2*2+prime(4)=4+7=11=prime(5), sod(2)=sod(11)=2, 11 is 2nd term

2*151+prime(5)=302+11=313=prime(65), sod(151)=sod(313)=7

2*5+prime(6)=10+13=23=prime(9), sod(5)=sod(23)=5, etc.

MATHEMATICA

f[n_] := Block[{p = 2}, While[q = 2 p + Prime[n + 2]; !PrimeQ@q || Plus @@ IntegerDigits@p != Plus @@ IntegerDigits@q, p = NextPrime@p]; q]; Array[f, 53]

EXTENSIONS

I removed all of the comments and added several examples and a Mathematica coding Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 23 2010

#1 by N. J. A. Sloane at Sun Jul 11 03:00:00 EDT 2010

NAME

Primes q from A178548.

DATA

31, 11, 313, 23, 163, 53, 157, 43, 41, 71, 103, 137, 61, 127, 193, 227, 113, 109, 107, 101, 277, 127, 101, 223, 113, 181, 251, 571, 233, 409, 151, 257, 211, 317, 491, 557, 661, 367, 433, 359, 313, 491, 271, 233, 509, 281, 241, 311, 271, 373, 1163, 613, 571

OFFSET

1,1

COMMENTS

See comments in A178548

2*13+prime(3)=26+5=31=prime(11), sod(13)=sod(31)=4

2*2+prime(4)=4+7=11=prime(5), sod(2)=sod(11)=2

2*151+prime(5)=302+11=313=prime(65), sod(151)=sod(313)=7

2*5+prime(6)=10+13=23=prime(9), sod(5)=sod(23)=5

2*73+prime(7)=146+17=163=prime(38), sod(73)=sod(163)=10

2*17+prime(8)=34+19=53=prime(16), sod(17)=sod(53)=8

2*67+prime(9)=134+23=157=prime(37), sod(67)=sod(157)=13

2*7+prime(10)=14+29=43=prime(14), sod(7)=sod(43)=7

2*5+prime(11)=10+31=41=prime(13), sod(5)=sod(41)=5

2*17+prime(12)=34+37=71=prime(20), sod(17)=sod(71)=8

2*31+prime(13)=62+41=103=prime(27), sod(31)=sod(103)=4

2*47+prime(14)=94+43=137=prime(33), sod(47)=sod(137)=11

2*7+prime(15)=14+47=61=prime(18), sod(7)=sod(61)=7

2*37+prime(16)=74+53=127=prime(31), sod(37)=sod(127)=10

2*67+prime(17)=134+59=193=prime(44), sod(57)=sod(193)=13

2*83+prime(18)=166+61=227=prime(49), sod(83)=sod(227)=11

2*23+prime(19)=46+67=113=prime(30), sod(23)=sod(113)=5

2*19+prime(20)=38+71=109=prime(29), sod(19)=sod(109)=10

2*17+prime(21)=34+73=107=prime(28), sod(17)=sod(107)=8

2*11+prime(22)=22+79=101=prime(26), sod(11)=sod(101)=2

2*97+prime(23)=194+83=277=prime(59), sod(97)=sod(277)=16

2*19+prime(24)=38+89=127=prime(31), sod(19)=sod(127)=10

2*2+prime(25)=4+97=101=prime(26), sod(2)=sod(101)=2

2*61+prime(26)=122+101=223=prime(48), sod(61)=sod(223)=7

2*5+prime(27)=10+103=113=prime(30), sod(5)=sod(113)=5

2*37+prime(28)=74+107=181=prime(42), sod(37)=sod(181)=10

2*71+prime(29)=142+109=251=prime(54), sod(71)=sod(251)=8

2*229+prime(30)=458+113=571=prime(105), sod(229)=sod(571)=13

2*53+prime(31)=106+127=233=prime(51), sod(53)=sod(233)=8

2*139+prime(32)=278+131=409=prime(80), sod(139)=sod(409)=13

2*7+prime(33)=14+137=151=prime(36), sod(7)=sod(151)=7

2*59+prime(34)=118+139=257=prime(55), sod(59)=sod(257)=14

2*31+prime(35)=62+149=211=prime(47), sod(31)=sod(211)=4

2*83+prime(36)=166+151=317=prime(66), sod(83)=sod(317)=11

2*167+prime(37)=334+157=491=prime(94), sod(167)=sod(491)=14

2*197+prime(38)=394+163=557=prime(102), sod(197)=sod(557)=17

2*247+prime(39)=494+167=661=prime(121), sod(247)=sod(661)=13

2*97+prime(40)=194+173=367=prime(73), sod(97)=sod(367)=16

2*127+prime(41)=254+179=433=prime(84), sod(127)=sod(433)=10

2*89+prime(42)=178+181=359=prime(77), sod(89)=sod(359)=17

2*61+prime(43)=122+191=313=prime(65), sod(61)=sod(313)=7

2*149+prime(44)=298+193=491=prime(94), sod(149)=sod(491)=14

2*37+prime(45)=74+197=271=prime(58), sod(37)=sod(271)=10

2*17+prime(46)=34+199=233=prime(51), sod(17)=sod(233)=8

2*149+prime(47)=298+211=509=prime(97), sod(149)=sod(509)=14

2*29+prime(48)=58+223=281=prime(60), sod(29)=sod(281)=11

2*7+prime(49)=14+227=241=prime(53), sod(7)=sod(241)=7

2*41+prime(50)=82+229=311=prime(64), sod(41)=sod(311)=5

2*19+prime(51)=38+233=271=prime(58), sod(19)=sod(271)=10

2*67+prime(52)=134+239=373=prime(74), sod(67)=sod(373)=13

2*461+prime(53)=922+241=1163=prime(192), sod(461)=sod(1163)=11

2*181+prime(54)=362+251=613=prime(112), sod(181)=sod(613)=10

2*157+prime(55)=314+257=571=prime(105), sod(157)=sod(571)=13

2*97+prime(56)=394+263=457=prime(88), sod(97)=sod(457)=16

2*19+prime(57)=38+269=307=prime(63), sod(19)=sod(307)=10

2*89+prime(58)=178+271=449=prime(87), sod(89)=sod(449)=17

2*83+prime(59)=166+277=443=prime(86), sod(83)=sod(443)=11

2*79+prime(60)=158+281=439=prime(85), sod(79)=sod(439)=16

2*167+prime(61)=354+283=617=prime(113), sod(167)=sod(617)=14

2*139+prime(62)=278+293=571=prime(105), sod(139)=sod(571)=13

2*107+prime(63)=214+307=521=prime(98), sod(107)=sod(521)=8

2*453+prime(64)=906+311=1217=prime(199), sod(453)=sod(1217)=13

2*353+prime(65)=706+313=1019=prime(171), sod(353)=sod(1019)=11

2*7+prime(66)=14+317=331=prime(67), sod(7)=sod(331)=7

2*443+prime(67)=886+331=1217=prime(199), sod(443)=sod(1217)=11

2*491+prime(68)=982+337=1319=prime(215), sod(491)=sod(1319)=14

2*157+prime(69)=314+347=661=prime(121), sod(157)=sod(661)=13

2*47+prime(70)=94+349=443=prime(86), sod(47)=sod(443)=11

2*97+prime(71)=194+353=547=prime(101), sod(97)=sod(547)=16

2*37+prime(72)=74+359=433=prime(84), sod(37)=sod(433)=10

EXAMPLE

i=1: 2*13+prime(3)=26+5=31=prime(11), sod(13)=sod(31)=4, 31 is first term

i=2: 2*2+prime(4)=4+7=11=prime(5), sod(2)=sod(11)=2, 11 is 2nd term

CROSSREFS

Cf. A000040, A001358, A178548

KEYWORD

base,nonn

AUTHOR

Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 29 2010

STATUS

approved