A326236 Numbers k such that N = k^6 is a twin rank (cf. A002822: 6N +- 1 are twin primes).

1, 1820, 2590, 4795, 5565, 8330, 8470, 10640, 10710, 15960, 16730, 19145, 24535, 26460, 34580, 37065, 41510, 42630, 43505, 48230, 59675, 69160, 84910, 90860, 99540, 103320, 112560, 114205, 117600, 127120, 129220, 131670, 143290, 152740, 161105, 164115, 170030, 175105, 181195, 185045

Offset: 1

Author

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

Keywords

• nonn

Comments

Dinculescu notes that when N = m^2 (resp. m^3) > 1 is a twin rank (i.e., in A002822), then m is a multiple of 5 (resp. of 7), cf. A326232 and A326234. Thus, when N = m^6, then m is a multiple of 35. See A326235 for a(n)/35, n > 1.

See A326232 and A326231 for m^2, A326234 and A326233 for m^3.

Links

• M. F. Hasler, Table of n, a(n) for n = 1..10001 (3667 terms from A. Dinculescu).
• 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, A326235 (a(n)/35, n>1), A326231, A326232 (analog for n^2), A326233, A326234 (analog for n^3), A326230 (least twin rank n^k for given k).

Programs

PARI

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

Formula

a(n) = 35*A326235(n-1), n >= 2.