%I #20 Mar 24 2017 21:15:42

%S 2,3,7,47,97,241,5051,204329,217069,29002021,190346677,3568762019,

%T 221167421,18725346527

%N Smallest prime p such that A005117(k+1) - A005117(k-1) = n, where p = A005117(k) for some k.

%e 2 is in this sequence because A005117(2+1) - A005117(2-1) = 3 - 1 = 2, where A005117(2) = 2 is prime for k = 2.

%e 3 is in this sequence because A005117(3+1) - A005117(3-1) = 5 - 2 = 3, where A005117(3) = 3 is prime for k = 3.

%e 7 is in this sequence because A005117(6+1) - A005117(6-1) = 10 - 6 = 4, where A005117(6) = 7 is prime for k = 6.

%e 47 is in this sequence because A005117(31+1) - A005117(31-1) = 51 - 46 = 5, where A005117(31) = 47 is prime for k = 31.

%e 97 is in this sequence because A005117(61+1) - A005117(61-1) = 101 - 95 = 6, where A005117(61) = 97 is prime for k = 61.

%e 241 is in this sequence because A005117(150+1) - A005117(150-1) = 246 - 239 = 7, where A005117(150) = 241 is prime for k = 150.

%e 5051 is in this sequence because A005117(3071+1) - A005117(3071-1) = 5053 - 5045 = 8, where A005117(3071) = 5051 is prime for k = 3071.

%t s = Select[Range[10^6], SquareFreeQ]; Table[k = 1; While[Nand[PrimeQ@ Set[p, s[[k]]], s[[k + 1]] - s[[k - 1]] == n], k++]; p, {n, 2, 10}] (* _Michael De Vlieger_, Mar 18 2017 *)

%Y Cf. A000040, A005117 (squarefree numbers), A067535, A070321.

%K nonn,more

%O 2,1

%A _Juri-Stepan Gerasimov_, Mar 17 2017

%E a(10) from _Michael De Vlieger_, Mar 18 2017

%E a(11)-a(15) from _Giovanni Resta_, Mar 22 2017