A330366 Prime numbers p_k such that p_k == 1 (mod 10) and p_(k+1) == 1 (mod 10).

181, 241, 421, 631, 691, 811, 1021, 1051, 1171, 1471, 1801, 2521, 2731, 3001, 3361, 3571, 4201, 4231, 4261, 4831, 4861, 5011, 5351, 5581, 5701, 5791, 6091, 6121, 6301, 6481, 6491, 6691, 6781, 7321, 8101, 8221, 8821, 8941, 9421, 9511, 9931, 10141, 10321, 10771, 11161, 11971

Offset: 1

Author

A.H.M. Smeets, Dec 12 2019

Keywords

• nonn

Links

• A.H.M. Smeets, Table of n, a(n) for n = 1..20000
• R. J. Lemke Oliver and K. Soundararajan, Unexpected biases in the distribution of consecutive primes, arXiv:1603.03720 [math.NT], 2016.
• R. J. Lemke Oliver and K. Soundararajan, Unexpected biases in the distribution of consecutive primes, Proceedings of the National Academy of Sciences of the United States of America, Vol. 113, No. 31 (2016), E4446-E4454.

Crossrefs

Cf. A030430 (1, any), this sequence (1, 1), A331555 (1, 3), A331324 (1, 7), A030431 (3, any), A030432 (7, any), A030433 (9, any) [where (a, b) means p_k == a (mod 10) and p_(k+1) == b (mod 10)].

Programs

Magma

[p: p in PrimesUpTo(14000)| (p mod 10 eq 1) and (NextPrime(p) mod 10 eq 1)]; // Marius A. Burtea, Jan 20 2020

Mathematica

First @ Transpose @ Select[Partition[Select[Range[13500], PrimeQ], 2, 1], Mod[First[#], 10] == 1 && Mod[Last[#],10] == 1 &] (* Amiram Eldar, Jan 20 2020 *)

PARI

isok(p) = isprime(p) && ((p % 10)==1) && ((nextprime(p+1) % 10) == 1); \\ Michel Marcus, Jan 20 2020