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A331324
Prime numbers p_k such that p_k == 1 (mod 10) and p_(k+1) == 7 (mod 10).
6
31, 61, 131, 151, 251, 271, 331, 541, 571, 601, 751, 941, 971, 991, 1181, 1231, 1291, 1321, 1361, 1601, 1621, 1741, 1831, 1861, 1901, 2011, 2131, 2221, 2251, 2281, 2341, 2351, 2371, 2411, 2441, 2551, 2671, 2791, 2851, 3061, 3121, 3181, 3301, 3391, 3511, 3541, 3631, 3691, 3761, 3911
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[4500], PrimeQ], 2, 1], Mod[First[#], 10] == 1 && Mod[Last[#], 10] == 7 &] (* Amiram Eldar, Jan 20 2020 *)
Prime[#]&/@SequencePosition[Mod[Prime[Range[600]], 10], {1, 7}][[All, 1]] (* Harvey P. Dale, Oct 17 2022 *)
PROG
(Magma) [p: p in PrimesUpTo(4400)| (p mod 10 eq 1) and (NextPrime(p) mod 10 eq 7)]; // Marius A. Burtea, Jan 20 2020
CROSSREFS
Cf. A030430 (1, any), A330366 (1, 1), A331555 (1, 3), this sequence (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: A054804 A128470 A195744 * A326896 A132230 A136066
KEYWORD
nonn
AUTHOR
A.H.M. Smeets, Jan 20 2020
STATUS
approved