%I #15 Jul 03 2015 06:18:13

%S 60,828,858,1032,1050,1230,1320,1878,2028,2340,3252,3390,3462,4548,

%T 5502,6870,6948,7590,7878,8010,9438,9720,9858,10038,10068,10302,11490,

%U 11718,13932,14388,15138,15270,15288,16068,16188,16230,17208,17292,17838,17910

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

%C Conjecture: The sequence contains infinitely many terms.

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

%C Subsequence of A014574.

%D 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.

%H Zhi-Wei Sun, <a href="/A259539/b259539.txt">Table of n, a(n) for n = 1..10000</a>

%H Zhi-Wei Sun, <a href="http://arxiv.org/abs/1402.6641">Problems on combinatorial properties of primes</a>, arXiv:1402.6641 [math.NT], 2014.

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

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

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

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

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, Jun 30 2015