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A331555 Prime numbers p_k such that p_k == 1 (mod 10) and p_(k+1) == 3 (mod 10). 6
11, 41, 71, 101, 191, 211, 281, 311, 431, 461, 521, 641, 661, 821, 881, 1031, 1061, 1091, 1151, 1201, 1301, 1451, 1481, 1511, 1531, 1721, 1811, 1871, 1931, 1951, 2081, 2111, 2141, 2311, 2381, 2591, 2621, 2711, 2801, 3191, 3251, 3331, 3371, 3461, 3581, 3671, 3821, 3851, 3931 (list; graph; refs; listen; history; text; internal format)
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.
MAPLE
filter:= p -> isprime(p) and nextprime(p) mod 10 = 3:
select(filter, [seq(i, i=1..4000, 10)]); # Robert Israel, Feb 20 2020
MATHEMATICA
First @ Transpose @ Select[Partition[Select[Range[4500], PrimeQ], 2, 1], Mod[First[#], 10] == 1 && Mod[Last[#], 10] == 3 &] (* Amiram Eldar, Jan 20 2020 *)
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 *)
PROG
(PARI) isok(p) = isprime(p) && ((p % 10)==1) && ((nextprime(p+1) % 10) == 3); \\ Michel Marcus, Jan 20 2020
(Magma) [p: p in PrimesUpTo(4500)| (p mod 10 eq 1) and (NextPrime(p) mod 10 eq 3)]; // Marius A. Burtea, Jan 20 2020
CROSSREFS
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)].
Contains A282321.
Sequence in context: A128467 A238713 A132232 * A282321 A031389 A178495
KEYWORD
nonn
AUTHOR
A.H.M. Smeets, Jan 20 2020
STATUS
approved

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Last modified March 1 16:12 EST 2024. Contains 370442 sequences. (Running on oeis4.)