A367318 -id:A367318 - cp's OEIS frontend

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

Jianing Song, Nov 01 2024

nonn

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

			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.

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

Cf. A115591, A002822, A367318, A319250.

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

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

cp's OEIS Frontend

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

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