A326231 - OEIS

A326231

Numbers n such that N = (5n)^2 is a twin rank (cf. A002822: 6N +- 1 are twin primes).

1, 2, 7, 12, 14, 15, 42, 48, 77, 86, 89, 99, 118, 131, 146, 161, 163, 167, 201, 208, 209, 246, 278, 286, 306, 334, 343, 370, 378, 384, 400, 404, 420, 422, 449, 462, 481, 483, 499, 509, 537, 551, 568, 587, 590, 609, 651, 652, 667, 684, 730, 755, 761, 806, 817, 825, 827, 848, 867, 870, 882, 916, 931, 980, 982, 992

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OFFSET

1,2

COMMENTS

Dinculescu notes that if N = m^2 > 1 is a twin rank (i.e., in A002822), then m is always a multiple of 5, and if N = m^3 > 1, then m is a multiple of 7, cf. A326234. He asks whether there are other pairs (a, b) different from (5, 2) and (7, 3) such that all twin ranks m^b > 1 are of the form m = a*n. (Of course (5, 2) and (7, 3) imply that (5, 2k), (7, 3k) and (35, 6k) is such a pair for any k.) This sequence lists the n for (a, b) = (5, 2), see A326232 for the numbers m.

See A326233, A326234 for m^3 and A326235, A326236 for m^6.

LINKS

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.

FORMULA

a(n) = A326232(n+1)/5.

PROG

(PARI) select( is(n)=!for(s=1, 2, ispseudoprime(150*n^2+(-1)^s)||return), [1..10^3])

CROSSREFS

Cf. A002822, A326232 ({1} U {5*a(n)}), A326233 (analog for m^3), A326234, A326235 (analog for m^6), A326230 (least twin rank n^k > 1 for given k).

Sequence in context: A174539 A049409 A287580 * A190548 A187971 A190486

Adjacent sequences: A326228 A326229 A326230 * A326232 A326233 A326234

KEYWORD

nonn

AUTHOR

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

STATUS

approved