A326232 Numbers k such that N = k^2 is a twin rank (cf. A002822: 6N +- 1 are twin primes).

1, 5, 10, 35, 60, 70, 75, 210, 240, 385, 430, 445, 495, 590, 655, 730, 805, 815, 835, 1005, 1040, 1045, 1230, 1390, 1430, 1530, 1670, 1715, 1850, 1890, 1920, 2000, 2020, 2100, 2110, 2245, 2310, 2405, 2415, 2495, 2545, 2685, 2755, 2840, 2935, 2950, 3045, 3255, 3260, 3335, 3420, 3650, 3775, 3805

Offset

1,2

Comments

Dinculescu notes that when k^2 > 1 is a twin rank (i.e., in A002822), then k is always a multiple of 5, and if k^3 > 1 is a twin rank, it is divisible by 7. See A326231 for the terms > 1 divided by 5.

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

Links

A. Dinculescu, Table of n, a(n) for n = 1..10001

A. Dinculescu, On the Numbers that Determine the Distribution of Twin Primes, Surveys in Mathematics and its Applications, 13 (2018), 171-181.

Prog

(PARI) select( is(n)=!for(s=1, 2, ispseudoprime(6*n^2+(-1)^s)||return), [1..5000])

Crossrefs

Cf. A002822, A326231 (a(n)/5, n>1), A326233, A326234 (analog for k^3), A326235, A326236 (analog for k^6), A326230 (least twin rank m^n for given n).

Sequence in context: A121158 A214650 A032772 * A189732 A307607 A174933

Adjacent sequences: A326229 A326230 A326231 * A326233 A326234 A326235

Keyword

nonn

Author

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

Status

approved