A326235 Numbers k such that N = (35k)^6 is a twin rank (A002822: 6N +- 1 are twin primes).

52, 74, 137, 159, 238, 242, 304, 306, 456, 478, 547, 701, 756, 988, 1059, 1186, 1218, 1243, 1378, 1705, 1976, 2426, 2596, 2844, 2952, 3216, 3263, 3360, 3632, 3692, 3762, 4094, 4364, 4603, 4689, 4858, 5003, 5177, 5287, 5361, 5426, 5999, 6054, 6285, 6347, 6417, 6457, 6639, 6862, 7269, 7500

Offset: 1

Author

M. F. Hasler and Antonie Dinculescu, Jun 14 2019

Keywords

• nonn

Comments

Dinculescu notes that if N = m^2 > 1 is a twin rank (i.e., in A002822), then m is a multiple of 5, and if N = m^3 > 1, then m is a multiple of 7, cf. A326231 and A326233. Thus, when N = m^6, then m is a multiple of 35, and here we list these m/35.

See A326236 for the numbers m.

Links

• A. Dinculescu and M. F. Hasler, Table of n, a(n) for n = 1..10000
• A. Dinculescu, On the Numbers that Determine the Distribution of Twin Primes, Surveys in Mathematics and its Applications, 13 (2018), 171-181.

Crossrefs

Cf. A002822, A326231 (analog for m^2), A326232, A326233 (analog for m^3), A326234, A326236 ({1} U {35*a(n)}), A326230 (least twin rank m^n for given n).

Programs

PARI

select( is(n)=!for(s=1,2,ispseudoprime(6*(35*n)^6+(-1)^s)||return), [1..10^4])

Formula

a(n) = A326236(n+1)/35.

Extensions

a(1..10^4) independently computed using Mathematica and PARI/GP, by A. D. and M. F. Hasler, Jun 19 2019