|
%I #17 Jun 10 2024 13:34:43
%S 401,491,701,761,911,1381,1571,2161,2531,2741,2861,2971,3011,3041,
%T 3221,3271,3491,3701,3881,4751,5051,5171,6011,6221,6451,6521,6581,
%U 7151,7351,7621,7691,8171,8191,8681,8761,8971,9311,9941,10151,10391,10531,10631,10691
%N Prime numbers p_k such that p_k == 1 (mod 10) and p_(k+1) == 9 (mod 10).
%H Robert Israel, <a href="/A332674/b332674.txt">Table of n, a(n) for n = 1..10000</a>
%H R. J. Lemke Oliver and K. Soundararajan, <a href="http://arxiv.org/abs/1603.03720">Unexpected biases in the distribution of consecutive primes</a>, arXiv:1603.03720 [math.NT], 2016.
%H R. J. Lemke Oliver and K. Soundararajan, <a href="https://doi.org/10.1073/pnas.1605366113">Unexpected biases in the distribution of consecutive primes</a>, Proceedings of the National Academy of Sciences of the United States of America, Vol. 113, No. 31 (2016), E4446-E4454.
%p select(p -> isprime(p) and nextprime(p) mod 10 = 9, [seq(i,i=1..20000,10)]); # _Robert Israel_, Jun 10 2024
%t First @ Transpose @ Select[Partition[Select[Range[12500], PrimeQ], 2, 1], Mod[First[#], 10] == 1 && Mod[Last[#], 10] == 9 &] (* _Amiram Eldar_, Feb 19 2020 *)
%o (PARI) forprime(p=1+o=2,1e4,p%10==9&&o%10==1&&print1(o",");o=p) \\ _M. F. Hasler_, Feb 19 2020
%Y 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)].
%K nonn
%O 1,1
%A _A.H.M. Smeets_, Feb 19 2020
|
