A333743 -id:A333743 - cp's OEIS frontend

A333744 Odd numbers k such that the multiplicative orders of 2 modulo k, k+2 and k+4 are equal.

3757261, 10440301, 24906181, 35391061, 35781661, 38921941, 40890541, 51661261, 67342981, 75938701, 76528741, 79017061, 91043101, 124464181, 149911141, 151954501, 152670541, 152698681, 162179581, 177779461, 184238581, 190380061, 199495741, 228968581, 230833441

Offset: 1

Amiram Eldar, Apr 03 2020

nonn

			3757261 is a term since the multiplicative orders of 2 modulo 3757261, 3757263 and 3757265 are all equal to 250484.

Amiram Eldar, Table of n, a(n) for n = 1..400
Eric Weisstein's World of Mathematics, Multiplicative Order.
Wikipedia, Multiplicative order.

Cf. A002326, A333743.

f[n_] := MultiplicativeOrder[2, n]; f1 = f[1]; f2 = f[3]; seq = {}; Do[f3 = f[n]; If[f1 == f2 && f2 == f3, AppendTo[seq, n - 4]]; f1 = f2; f2 = f3, {n, 5, 10^8, 2}]; seq

A367318 Lesser of twin primes p such that p and p+2 are both in A115591.

Original entry on oeis.org

191, 311, 1487, 1871, 2711, 2999, 3167, 3767, 4967, 5519, 7559, 8087, 10271, 11351, 11831, 13679, 15647, 18311, 18911, 21647, 22271, 22367, 23687, 25799, 26711, 27239, 27527, 27791, 29399, 29879, 31727, 31847, 33287, 34367, 35591, 38447, 38567, 40127, 40847, 42071

Offset: 1

Amiram Eldar, Nov 14 2023

nonn

Primes p such that p+2 is also a prime and (p-1)/ord(2, p) = (p+1)/ord(2, p+2) = 2, where ord(2,k) is the multiplicative order of 2 modulo k.
Equivalently, lesser of twin primes p such that ord(2, p+2) = ord(2, p) + 1,
Equal consecutive values in A001917 that correspond to twin primes (p, p+2) are either 1 if p is in A319248, or 2 if p is in this sequence.
Terms are congruent to 23 modulo 24. - Jianing Song, Nov 01 2024

Amiram Eldar, Table of n, a(n) for n = 1..10000

Subsequence of A001359 and A115591.

Cf. A001122, A001917, A002326, A014664, A319248, A333743.

Select[Prime[Range[2, 4400]], PrimeQ[# + 2] && MultiplicativeOrder[2, # + 2] == MultiplicativeOrder[2, #] + 1 &]

is(n) = isprime(n) && isprime(n+2) && znorder(Mod(2, n + 2)) == znorder(Mod(2, n)) + 1;

cp's OEIS Frontend

A333744 Odd numbers k such that the multiplicative orders of 2 modulo k, k+2 and k+4 are equal.

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