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%I #10 Oct 01 2013 17:57:35
%S 49,121,841,961,1849,22801,24649,36481,43681,47089,48841,69169,96721,
%T 128881,134689,165649,243049,284089,316969,319225,405769,609961,
%U 664225,677329,707281,737881,776161,863041,919681,994009,1026169,1038361
%N Squares that are the sum of 3 consecutive primes.
%C Sum of reciprocals converges to 0.0317...
%H Charles R Greathouse IV, <a href="/A080665/b080665.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A076304(n)^2. - _Zak Seidov_, May 26 2013
%e 13+17+19 = 49
%t 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
%o (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) }
%o (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
%Y Cf. A062703.
%K nonn,easy
%O 1,1
%A _Cino Hilliard_, Mar 02 2003
%E Edited and extended by _Robert G. Wilson v_, Mar 02 2003
%E Offset corrected by _Zak Seidov_, May 26 2013
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