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

1,1

Comments

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

Links

Table of n, a(n) for n=1..49.

Example

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.

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 *)

Crossrefs

Cf. A165285

Sequence in context: A080822 A068363 A351377 * A031342 A215166 A141870

Adjacent sequences: A165283 A165284 A165285 * A165287 A165288 A165289

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Sep 13 2009

Extensions

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

Status

approved