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 A080665 Squares that are the sum of 3 consecutive primes. 6
 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 (list; graph; refs; listen; history; text; internal format)
 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: A227863 A115557 A167718 * A130007 A202331 A287005 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

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Last modified January 29 07:03 EST 2020. Contains 331337 sequences. (Running on oeis4.)