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

1,1

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

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 *)

Prog

(PARI) isok(p) = isprime(p) && ((p % 10)==1) && ((nextprime(p+1) % 10) == 3); \\ Michel Marcus, Jan 20 2020
(Magma) [p: p in PrimesUpTo(4500)| (p mod 10 eq 1) and (NextPrime(p) mod 10 eq 3)]; // Marius A. Burtea, Jan 20 2020

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.

Sequence in context: A128467 A238713 A132232 * A282321 A031389 A178495

Adjacent sequences: A331552 A331553 A331554 * A331556 A331557 A331558

Keyword

nonn

Author

A.H.M. Smeets, Jan 20 2020

Status

approved