A331555 - OEIS

%I #28 Sep 08 2022 08:46:25

%S 11,41,71,101,191,211,281,311,431,461,521,641,661,821,881,1031,1061,

%T 1091,1151,1201,1301,1451,1481,1511,1531,1721,1811,1871,1931,1951,

%U 2081,2111,2141,2311,2381,2591,2621,2711,2801,3191,3251,3331,3371,3461,3581,3671,3821,3851,3931

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

%H Robert Israel, <a href="/A331555/b331555.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 filter:= p -> isprime(p) and nextprime(p) mod 10 = 3:

%p select(filter, [seq(i,i=1..4000,10)]); # _Robert Israel_, Feb 20 2020

%t First @ Transpose @ Select[Partition[Select[Range[4500], PrimeQ], 2, 1], Mod[First[#], 10] == 1 && Mod[Last[#],10] == 3 &] (* _Amiram Eldar_, Jan 20 2020 *)

%t 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 *)

%o (PARI) isok(p) = isprime(p) && ((p % 10)==1) && ((nextprime(p+1) % 10) == 3); \\ _Michel Marcus_, Jan 20 2020

%o (Magma) [p: p in PrimesUpTo(4500)| (p mod 10 eq 1) and (NextPrime(p) mod 10 eq 3)]; // _Marius A. Burtea_, Jan 20 2020

%Y 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)].

%Y Contains A282321.

%K nonn

%O 1,1

%A _A.H.M. Smeets_, Jan 20 2020