A319250 Numbers k such that 24k + 11 and 24k + 13 are a pair of twin primes in A001122.

0, 2, 7, 14, 17, 27, 34, 60, 67, 69, 84, 94, 144, 160, 167, 170, 177, 199, 282, 284, 289, 314, 342, 345, 367, 392, 419, 420, 422, 437, 452, 510, 525, 580, 599, 609, 619, 669, 674, 707, 724, 739, 797, 854, 865, 875, 895, 899, 900, 942, 952, 959, 984, 1004, 1080

Offset

1,2

Comments

Numbers k such that 24k + 11 and 24k + 13 are both in A001122. See A319248 and A319249 for detailed information.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..405 from Jianing Song)

Formula

a(n) = (A319248(n+1) - 11)/24 = (A319249(n+1) - 13)/24.

Example

11 and 13 are a pair of twin primes both having 2 as a primitive root, so 0 is a term.
59 and 61 are a pair of twin primes both having 2 as a primitive root, so 2 is a term.
Although 227 and 229 are a pair of twin primes, neither of them has 2 as a primitive root, so 9 is not a term.

Mathematica

Select[Range[0, 1080], PrimeQ[24*# + 11] && PrimeQ[24*# + 13] && PrimitiveRoot[24*# + 11] == 2 && PrimitiveRoot[24*# + 13] == 2 &] (* Amiram Eldar, May 02 2023 *)

Prog

(PARI) for(k=0, 1000, if(znorder(Mod(2, 24*k+11))==24*k+10 && znorder(Mod(2, 24*k+13))==24*k+12, print1(k, ", ")))

Crossrefs

Cf. A001122, A002822, A319248, A319249.

Sequence in context: A247866 A057126 A363026 * A018349 A256798 A228831

Adjacent sequences: A319247 A319248 A319249 * A319251 A319252 A319253

Keyword

nonn

Author

Jianing Song, Sep 15 2018

Status

approved