A332674 Prime numbers p_k such that p_k == 1 (mod 10) and p_(k+1) == 9 (mod 10).

401, 491, 701, 761, 911, 1381, 1571, 2161, 2531, 2741, 2861, 2971, 3011, 3041, 3221, 3271, 3491, 3701, 3881, 4751, 5051, 5171, 6011, 6221, 6451, 6521, 6581, 7151, 7351, 7621, 7691, 8171, 8191, 8681, 8761, 8971, 9311, 9941, 10151, 10391, 10531, 10631, 10691

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

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.

Maple

select(p -> isprime(p) and nextprime(p) mod 10 = 9, [seq(i, i=1..20000, 10)]); # Robert Israel, Jun 10 2024

Mathematica

First @ Transpose @ Select[Partition[Select[Range[12500], PrimeQ], 2, 1], Mod[First[#], 10] == 1 && Mod[Last[#], 10] == 9 &] (* Amiram Eldar, Feb 19 2020 *)

Prog

(PARI) forprime(p=1+o=2, 1e4, p%10==9&&o%10==1&&print1(o", "); o=p) \\ M. F. Hasler, Feb 19 2020

Crossrefs

Cf. A030430 (1, any), A330366 (1, 1), A331555 (1, 3), A331324 (1, 7), this sequence (1, 9), A030431 (3, any), A332675 (3, 1), A332676 (3, 3), 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: A159890 A029705 A096991 * A141026 A158313 A094614

Adjacent sequences: A332671 A332672 A332673 * A332675 A332676 A332677

Keyword

nonn

Author

A.H.M. Smeets, Feb 19 2020

Status

approved