A165286 Primes which are the sum of two or more consecutive terms of A072055.

23, 61, 83, 101, 139, 157, 197, 263, 283, 293, 331, 349, 367, 383, 401, 449, 491, 509, 541, 569, 571, 577, 641, 659, 661, 701, 751, 773, 809, 811, 853, 859, 881, 887, 967, 977, 997, 1009, 1039, 1069, 1117, 1123, 1181, 1193, 1217, 1237, 1279, 1283, 1361

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Sep 13 2009

Keywords

• nonn

Comments

The terms in A072055 are odd, so the count of terms in the sum must be odd to yield a prime.

Examples

			a(1)= 5+7+11 = sum_{i=1..3} A072055(i) = 23.
a(2) = sum_{i=1..5} A072055(i) = 5+7+11+15+23 = 61. a(3) = 7+11+15+23+27 = 83.
		

Crossrefs

Cf. A165285

Programs

Mathematica

lst={};Do[s=2*Prime[m]+1;Do[p=Prime[n];s+=(2*p+1);If[PrimeQ[s], If[s<=6949, AppendTo[lst,s]]],{n,m+1,6!}],{m,1,6!}];lst=Take[Union@lst,200]
Module[{nn=100,terms},terms=2*Prime[Range[nn]]+1;Take[Union[Select[ Flatten[ Table[Total/@Partition[terms,n,1],{n,3,nn,2}]],PrimeQ]],nn/2]] (* Harvey P. Dale, Jun 11 2015 *)

Extensions

Redefined in terms of A072055; cross-references to unrelated sequences deleted - R. J. Mathar, Sep 16 2009