A080665 Squares that are the sum of 3 consecutive primes.

49, 121, 841, 961, 1849, 22801, 24649, 36481, 43681, 47089, 48841, 69169, 96721, 128881, 134689, 165649, 243049, 284089, 316969, 319225, 405769, 609961, 664225, 677329, 707281, 737881, 776161, 863041, 919681, 994009, 1026169, 1038361

Offset

1,1

Comments

Sum of reciprocals converges to 0.0317...

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) = A076304(n)^2. - Zak Seidov, May 26 2013

Example

13+17+19 = 49

Mathematica

PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ[k], k-- ]; k]; NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; f[n_] := Block[{m = Floor[n/3], t = 1}, If[PrimeQ[m], s = PrevPrim[m] + m + NextPrim[m], s = PrevPrim[ PrevPrim[m]] + PrevPrim[m] + NextPrim[m]; t = PrevPrim[m] + NextPrim[m] + NextPrim[ NextPrim[m]]]; If[s == n || t == n, True, False]]; Select[ Range[1020], f[ #^2] &]^2

Prog

(PARI) sump1p2p3sq(n)= {sr=0; forprime(x=2, n, y=x+nextprime(x+1)+nextprime(nextprime(x+1)+1); if(issquare(y), print1(y" "); sr+=1.0/y; ) ); print(); print(sr) }
(PARI) for(n=1, 1e4, p=precprime(n^2/3); q=nextprime(p+1); t=n^2-p-q; if(isprime(t) && t==if(t>q, nextprime(q+1), precprime(p-1)), print1(n^2", "))) \\ Charles R Greathouse IV, May 26 2013

Crossrefs

Cf. A062703.

Sequence in context: A374290 A115557 A167718 * A130007 A378629 A202331

Adjacent sequences: A080662 A080663 A080664 * A080666 A080667 A080668

Keyword

nonn,easy

Author

Cino Hilliard, Mar 02 2003

Extensions

Edited and extended by Robert G. Wilson v, Mar 02 2003

Offset corrected by Zak Seidov, May 26 2013

Status

approved