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Search: id:A080665
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| A080665 |
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Squares that are the sum of 3 consecutive primes. |
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+0
2
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| 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; listen)
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OFFSET
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2,1
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COMMENT
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Sum of reciprocals converges to 0.0317...
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EXAMPLE
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13+17+19 = 49
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MATHEMATICA
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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
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PROGRAM
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(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) }
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CROSSREFS
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Cf. A062703.
Sequence in context: A084733 A115557 A167718 this_sequence A130007 A044300 A044681
Adjacent sequences: A080662 A080663 A080664 this_sequence A080666 A080667 A080668
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KEYWORD
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nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Mar 02 2003
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 02 2003
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