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

Author

Jianing Song, Sep 15 2018

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A001122, A002822, A319248, A319249.

Programs

Mathematica

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

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, ", ")))

Formula

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