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

Author

Cino Hilliard, Mar 02 2003

Keywords

• nonn
• easy

Comments

Sum of reciprocals converges to 0.0317...

Examples

			13+17+19 = 49
		

Links

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

Crossrefs

Cf. A062703.

Programs

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

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

Formula

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

Extensions

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

Offset corrected by Zak Seidov, May 26 2013