A377561 Numbers k such that 24k - 1 and 24k + 1 are a pair of twin primes in A115591.

8, 13, 62, 78, 113, 125, 132, 157, 207, 230, 315, 337, 428, 473, 493, 570, 652, 763, 788, 902, 928, 932, 987, 1075, 1113, 1135, 1147, 1158, 1225, 1245, 1322, 1327, 1387, 1432, 1483, 1602, 1607, 1672, 1702, 1753, 1767, 1845, 1880, 1973, 1992, 2083, 2155, 2212, 2220, 2233

Offset

1,1

Comments

Numbers k such that 24k - 1 is in A367318. Note that all terms there are congruent to 23 modulo 24.

Links

Jianing Song, Table of n, a(n) for n = 1..10000

Formula

a(n) = (A367318(n) + 1)/24.

Example

8 is a term since the multiplicative order of 2 modulo 24*8 - 1 = 191 is 95, and the multiplicative order of 2 modulo 24*8 + 1 = 193 is 96.

Prog

(PARI) isA377561(k) = znorder(Mod(2, 24*k-1))==12*k-1 && znorder(Mod(2, 24*k+1))==12*k \\ No need to check primality as the multiplicative order of 2 modulo a composite odd number m cannot be equal to (m-1)/2; see my comment in A001567

Crossrefs

Cf. A115591, A002822, A367318, A319250.

Sequence in context: A081966 A316527 A304546 * A166670 A107764 A306131

Adjacent sequences: A377558 A377559 A377560 * A377562 A377563 A377564

Keyword

nonn

Author

Jianing Song, Nov 01 2024

Status

approved