A332676 Prime numbers p_k such that p_k == 3 (mod 10) and p_(k+1) == 3 (mod 10).

283, 1153, 1723, 2053, 2143, 3413, 3583, 3823, 3853, 4243, 4273, 4363, 4483, 4663, 5323, 5903, 6133, 6163, 6343, 6553, 6793, 6803, 7253, 7963, 8243, 8353, 8543, 8563, 8783, 8893, 9283, 9403, 10223, 10303, 10433, 10993, 11093, 11383, 12253, 12703, 13063, 13513, 13933, 14293, 14983

Offset: 1

Author

A.H.M. Smeets, Feb 19 2020

Keywords

• nonn

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.

Crossrefs

Cf. A030430 (1, any), A330366 (1, 1), A331555 (1, 3), A331324 (1, 7), A332674 (1, 9), A030431 (3, any), A332675 (3, 1), this sequence (3, 3), A030432 (7, any), A030433 (9, any) [where (a, b) means p_k == a (mod 10) and p_(k+1) == b (mod 10)].

Programs

Maple

filter:= t -> isprime(t) and nextprime(t) mod 10 = 3:
select(filter, [seq(i,i=3..20000,10)]); # Robert Israel, May 08 2020

Mathematica

First @ Transpose @ Select[Partition[Select[Range[20000], PrimeQ], 2, 1], Mod[First[#], 10] == 3 && Mod[Last[#], 10] == 3 &] (* Amiram Eldar, Feb 19 2020 *)