A326234 Numbers n such that N = n^3 is a twin rank (A002822: 6N +- 1 are twin primes).

1, 28, 42, 168, 203, 287, 308, 518, 1043, 1057, 1512, 1603, 1638, 1680, 1757, 1988, 2905, 3367, 3927, 4018, 4928, 5033, 5145, 5257, 5292, 5432, 5733, 6762, 7182, 7210, 7798, 8715, 10213, 10318, 10668, 10745, 11088, 12243, 13552, 14245, 14588, 14707, 15155, 15323, 15687, 15722, 15757

Offset: 1

Author

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

Keywords

• nonn

Comments

Dinculescu notes that when n^2 or n^3 is a twin rank > 1 (i.e., in A002822), then n is a multiple of 5, resp. 7. It is unknown whether there exist other pairs (a, b) different from (5, 2) and (7, 3) such that n^b => a | n. (Of course (5, 2k) and (7, 3k) and (35, 6k) is a solution for any k.) See A326233 for the terms > 1 divided by 7.

See A326232 and A326231 for the case n^2, A326236 and A326235 for n^6.

Links

• A. Dinculescu, Table of n, a(n) for n = 1..14709
• 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, A326233 (a(n)/7, n>1), A326231, A326232 (analog for n^2), A326235, A326236 (analog for n^6), A326230 (least twin rank n^k > 1 for given k).

Programs

PARI

select( is(n)=!for(s=1,2,ispseudoprime(6*n^3+(-1)^s)||return), [1..10^5])

Formula

a(n) = 7*A326233(n-1), n >= 2.