A332676 -id:A332676 - cp's OEIS frontend

A332674 Prime numbers p_k such that p_k == 1 (mod 10) and p_(k+1) == 9 (mod 10).

401, 491, 701, 761, 911, 1381, 1571, 2161, 2531, 2741, 2861, 2971, 3011, 3041, 3221, 3271, 3491, 3701, 3881, 4751, 5051, 5171, 6011, 6221, 6451, 6521, 6581, 7151, 7351, 7621, 7691, 8171, 8191, 8681, 8761, 8971, 9311, 9941, 10151, 10391, 10531, 10631, 10691

Offset: 1

A.H.M. Smeets, Feb 19 2020

nonn

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.

Cf. A030430 (1, any), A330366 (1, 1), A331555 (1, 3), A331324 (1, 7), this sequence (1, 9), A030431 (3, any), A332675 (3, 1), A332676 (3, 3), A030432 (7, any), A030433 (9, any) [where (a, b) means p_k == a (mod 10) and p_(k+1) == b (mod 10)].

select(p -> isprime(p) and nextprime(p) mod 10 = 9, [seq(i,i=1..20000,10)]); # Robert Israel, Jun 10 2024

First @ Transpose @ Select[Partition[Select[Range[12500], PrimeQ], 2, 1], Mod[First[#], 10] == 1 && Mod[Last[#], 10] == 9 &] (* Amiram Eldar, Feb 19 2020 *)

forprime(p=1+o=2,1e4,p%10==9&&o%10==1&&print1(o",");o=p) \\ M. F. Hasler, Feb 19 2020

A332675 Prime numbers p_k such that p_k == 3 (mod 10) and p_(k+1) == 1 (mod 10).

Original entry on oeis.org

523, 683, 743, 983, 1163, 1193, 1373, 1523, 1733, 1823, 1913, 2003, 2153, 2213, 2243, 2273, 2503, 2663, 2843, 3623, 3803, 4373, 4423, 4463, 4583, 4603, 4703, 4733, 4943, 5483, 5573, 5693, 5783, 5813, 5953, 6113, 6143, 6203, 6473, 6833, 6983, 7393, 7433, 7673, 7883, 8093, 8513, 8573

Offset: 1

A.H.M. Smeets, Feb 19 2020

nonn

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.

Cf. A030430 (1, any), A330366 (1, 1), A331555 (1, 3), A331324 (1, 7), A332674 (1, 9), A030431 (3, any), this sequence (3, 1), A332676 (3, 3), A030432 (7, any), A030433 (9, any) [where (a, b) means p_k == a (mod 10) and p_(k+1) == b (mod 10)].

First @ Transpose @ Select[Partition[Select[Range[10^4], PrimeQ], 2, 1], Mod[First[#], 10] == 3 && Mod[Last[#], 10] == 1 &] (* Amiram Eldar, Feb 19 2020 *)

cp's OEIS Frontend

A332674 Prime numbers p_k such that p_k == 1 (mod 10) and p_(k+1) == 9 (mod 10).

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