The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A268304

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A268304

Odd numbers n such that binomial(6*n, 2*n) == -1 (mod 8).
(history; published version)

#11 by N. J. A. Sloane at Sun Feb 07 20:15:48 EST 2016

STATUS

proposed

approved

#10 by Michael De Vlieger at Sun Feb 07 09:27:58 EST 2016

STATUS

editing

proposed

#9 by Michael De Vlieger at Sun Feb 07 09:27:56 EST 2016

MATHEMATICA

Select[Range[1, 5000, 2], Mod[Binomial[6 #, 2 #], 8] == 7 &] (* Michael De Vlieger, Feb 07 2016 *)

STATUS

proposed

editing

#8 by Chai Wah Wu at Sun Feb 07 09:09:44 EST 2016

STATUS

editing

proposed

#7 by Chai Wah Wu at Fri Feb 05 20:10:17 EST 2016

PROG

from __future__ import division

m2[i+1] += m2[i] # Chai Wah Wu, Feb 05 2016

#6 by Chai Wah Wu at Fri Feb 05 20:09:50 EST 2016

LINKS

Chai Wah Wu, <a href="/A268304/b268304.txt">Table of n, a(n) for n = 1..10000</a>

PROG

(Python)

A268304_list, b, m1, m2 = [], 15, [21941965946880, -54854914867200, 49244258396160, -19011472727040, 2933960577120, -126898662960, 771887070, 385943535, 385945560], [10569646080, -25763512320, 22419210240, -8309145600, 1209116160, -46992960, 415800, 311850, 311850]

for n in range(10**3):

if b % 8 == 7:

A268304_list.append(2*n+1)

b = b*m1[-1]//m2[-1]

for i in range(8):

m1[i+1] += m1[i]

m2[i+1] += m2[i] # Chai Wah Wu, Feb 05 2016

STATUS

approved

editing

#5 by Bruno Berselli at Mon Feb 01 05:24:15 EST 2016

STATUS

reviewed

approved

#4 by Joerg Arndt at Sun Jan 31 12:12:16 EST 2016

STATUS

proposed

reviewed

#3 by Michel Marcus at Sun Jan 31 11:23:58 EST 2016

STATUS

editing

proposed

#2 by Michel Marcus at Sun Jan 31 11:06:13 EST 2016

NAME

allocated for Michel MarcusOdd numbers n such that binomial(6*n, 2*n) == -1 (mod 8).

DATA

1, 5, 21, 73, 85, 273, 293, 297, 329, 341, 529, 545, 1041, 1057, 1089, 1093, 1105, 1173, 1189, 1193, 1297, 1317, 1321, 1353, 1365, 2065, 2081, 2113, 2117, 2129, 2177, 2181, 2209, 2577, 2593, 4113, 4129, 4161, 4165, 4177, 4225, 4229, 4257, 4353, 4357, 4373, 4417, 4421, 4433

OFFSET

1,2

COMMENTS

The primes p of this sequence are those that give the even semiprimes of A268303.

LINKS

Marc Chamberland and Karl Dilcher, <a href="http://dx.doi.org/10.1016/j.jnt.2009.05.010">A Binomial Sum Related to Wolstenholme's Theorem</a>, J. Number Theory, Vol. 171, Issue 11 (Nov. 2009), pp. 2659-2672. See Table 2 p. 2669.

PROG

(PARI) isok(n) = (n%2) && Mod(binomial(6*n, 2*n), 8) == Mod(-1, 8);

CROSSREFS

Cf. A234839, A268303.

KEYWORD

allocated

nonn

AUTHOR

Michel Marcus, Jan 31 2016

STATUS

approved

editing