A181938 - OEIS

A181938

Isolated primes = 1 mod 6: sandwiched by primes = 5 mod 6.

7, 13, 19, 43, 97, 103, 109, 127, 139, 181, 193, 229, 241, 283, 307, 313, 349, 397, 409, 421, 457, 463, 487, 499, 643, 691, 709, 769, 787, 811, 823, 829, 853, 859, 877, 883, 907, 919, 937, 967, 1021, 1051, 1093, 1153, 1171, 1279, 1303, 1423, 1429, 1447, 1483

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OFFSET

1,1

COMMENTS

Primes p(m) = 1 mod 6 such that both p(m-1) and p(m+1) are congruent to 5 mod 6.

Corresponding indices m are 4, 6, 8, 14, 25, 27, 29, 31 (A181978).

Note that values of d = p(m+1) - p(m-1) are multiples of 6.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

EXAMPLE

7 = p(4) = 1 mod 6 and both p(3) = 5 and p(5) = 11 are congruent to 5 mod 6,

13 = p(6) = 1 mod 6 and both p(5) = 11 and p(7) = 17 are congruent to 5 mod 6,

43 = p(14) = 1 mod 6 and both p(13) = 41 and p(15) = 47 are congruent to 5 mod 6.

MATHEMATICA

Select[Prime[Range[2, 300]], Mod[#, 6] == 1 && Mod[NextPrime[#, -1], 6] == 5 && Mod[NextPrime[#, 1], 6] == 5 &] (* T. D. Noe, Apr 04 2012 *)

Transpose[Select[Partition[Prime[Range[250]], 3, 1], Mod[#[[1]], 6] == Mod[#[[3]], 6] == 5&&Mod[#[[2]], 6]==1&]][[2]] (* Harvey P. Dale, Sep 17 2012 *)

CROSSREFS

Cf. A002476, A039704, A055625, A181978, A210248.

Sequence in context: A249381 A040096 A358322 * A073648 A298737 A109558

Adjacent sequences: A181935 A181936 A181937 * A181939 A181940 A181941

KEYWORD

nonn

AUTHOR

Zak Seidov, Apr 03 2012

STATUS

approved