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

1,1

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.

Mathematica

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

Prog

(PARI) isok(p) = isprime(p) && ((p % 10)==1) && ((nextprime(p+1) % 10) == 1); \\ Michel Marcus, Jan 20 2020
(Magma) [p: p in PrimesUpTo(14000)| (p mod 10 eq 1) and (NextPrime(p) mod 10 eq 1)]; // Marius A. Burtea, Jan 20 2020

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)].

Sequence in context: A139648 A142519 A053140 * A107694 A142312 A020360

Adjacent sequences: A330363 A330364 A330365 * A330367 A330368 A330369

Keyword

nonn

Author

A.H.M. Smeets, Dec 12 2019

Status

approved