A259539 Numbers m with m-1, m+1 and prime(m)+2 all prime.

60, 828, 858, 1032, 1050, 1230, 1320, 1878, 2028, 2340, 3252, 3390, 3462, 4548, 5502, 6870, 6948, 7590, 7878, 8010, 9438, 9720, 9858, 10038, 10068, 10302, 11490, 11718, 13932, 14388, 15138, 15270, 15288, 16068, 16188, 16230, 17208, 17292, 17838, 17910

Offset

1,1

Comments

Conjecture: The sequence contains infinitely many terms.

This is stronger than the Twin Prime Conjecture, and weaker than the conjecture in A259540.

Subsequence of A014574.

References

Zhi-Wei Sun, Problems on combinatorial properties of primes, in: M. Kaneko, S. Kanemitsu and J. Liu (eds.), Number Theory: Plowing and Starring through High Wave Forms, Proc. 7th China-Japan Seminar (Fukuoka, Oct. 28-Nov. 1, 2013), Ser. Number Theory Appl., Vol. 11, World Sci., Singapore, 2015, pp. 169-187.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Zhi-Wei Sun, Problems on combinatorial properties of primes, arXiv:1402.6641 [math.NT], 2014.

Example

a(1) = 60 since 60-1 = 59, 60+1 = 61 and prime(60)+2 = 283 are all prime.

Mathematica

n=0; Do[If[PrimeQ[k-1]&&PrimeQ[k+1]&&PrimeQ[Prime[k]+2], n=n+1; Print[n, " ", k]], {k, 1, 18000}]

Prog

(PARI) lista(nn) = {forprime(p=2, nn, if (isprime(p+2) && isprime(prime(p+1)+2), print1(p+1, ", "))); } \\ Michel Marcus, Jun 30 2015

Crossrefs

Cf. A000040, A001359, A006512, A014574, A236458, A259540.

Sequence in context: A323566 A063011 A008357 * A138898 A229368 A305625

Adjacent sequences: A259536 A259537 A259538 * A259540 A259541 A259542

Keyword

nonn

Author

Zhi-Wei Sun, Jun 30 2015

Status

approved