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A330366
Prime numbers p_k such that p_k == 1 (mod 10) and p_(k+1) == 1 (mod 10).
6
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
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
KEYWORD
nonn
AUTHOR
A.H.M. Smeets, Dec 12 2019
STATUS
approved