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A326231 Numbers n such that N = (5n)^2 is a twin rank (cf. A002822: 6N +- 1 are twin primes). 8
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 24 02:56 EDT 2021. Contains 345415 sequences. (Running on oeis4.)