A331324 Prime numbers p_k such that p_k == 1 (mod 10) and p_(k+1) == 7 (mod 10).

31, 61, 131, 151, 251, 271, 331, 541, 571, 601, 751, 941, 971, 991, 1181, 1231, 1291, 1321, 1361, 1601, 1621, 1741, 1831, 1861, 1901, 2011, 2131, 2221, 2251, 2281, 2341, 2351, 2371, 2411, 2441, 2551, 2671, 2791, 2851, 3061, 3121, 3181, 3301, 3391, 3511, 3541, 3631, 3691, 3761, 3911

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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.

Mathematica

First @ Transpose @ Select[Partition[Select[Range[4500], PrimeQ], 2, 1], Mod[First[#], 10] == 1 && Mod[Last[#], 10] == 7 &] (* Amiram Eldar, Jan 20 2020 *)
Prime[#]&/@SequencePosition[Mod[Prime[Range[600]], 10], {1, 7}][[All, 1]] (* Harvey P. Dale, Oct 17 2022 *)

Prog

(Magma) [p: p in PrimesUpTo(4400)| (p mod 10 eq 1) and (NextPrime(p) mod 10 eq 7)]; // Marius A. Burtea, Jan 20 2020

Crossrefs

Cf. A030430 (1, any), A330366 (1, 1), A331555 (1, 3), this sequence (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)].

Sequence in context: A054804 A128470 A195744 * A326896 A132230 A136066

Adjacent sequences: A331321 A331322 A331323 * A331325 A331326 A331327

Keyword

nonn

Author

A.H.M. Smeets, Jan 20 2020

Status

approved