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A259539
Numbers m with m-1, m+1 and prime(m)+2 all prime.
6
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, 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
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Jun 30 2015
STATUS
approved