A331555 Prime numbers p_k such that p_k == 1 (mod 10) and p_(k+1) == 3 (mod 10).

11, 41, 71, 101, 191, 211, 281, 311, 431, 461, 521, 641, 661, 821, 881, 1031, 1061, 1091, 1151, 1201, 1301, 1451, 1481, 1511, 1531, 1721, 1811, 1871, 1931, 1951, 2081, 2111, 2141, 2311, 2381, 2591, 2621, 2711, 2801, 3191, 3251, 3331, 3371, 3461, 3581, 3671, 3821, 3851, 3931

Offset: 1

Author

A.H.M. Smeets, Jan 20 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), this sequence (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)].

Contains A282321.

Programs

Magma

[p: p in PrimesUpTo(4500)| (p mod 10 eq 1) and (NextPrime(p) mod 10 eq 3)]; // Marius A. Burtea, Jan 20 2020

Maple

filter:= p -> isprime(p) and nextprime(p) mod 10 = 3:
select(filter, [seq(i,i=1..4000,10)]); # Robert Israel, Feb 20 2020

Mathematica

First @ Transpose @ Select[Partition[Select[Range[4500], PrimeQ], 2, 1], Mod[First[#], 10] == 1 && Mod[Last[#],10] == 3 &] (* Amiram Eldar, Jan 20 2020 *)
Prime[#]&/@SequencePosition[Table[Which[Mod[n,10]==1, 1,Mod[n,10]==3,-1,True,0],{n,Prime[Range[600]]}],{1,-1}][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 10 2020 *)

PARI

isok(p) = isprime(p) && ((p % 10)==1) && ((nextprime(p+1) % 10) == 3); \\ Michel Marcus, Jan 20 2020