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Search: id:A077280
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| A077280 |
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Sum of next a(n) successive primes is a square. |
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4
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OFFSET
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1,1
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COMMENT
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Partition the sequence of primes into groups so that sum of terms in each group is a square: {2-23}, {29-1021}, {1031-2179}, {2203-4051}, {4057-4153}, {4157-50377}, {50383-66643}, {66653-173647}, {173651-2076913}, {2076917-???}, ...
A077280(n) gives the number of terms in n-th group; A077281(n)^2 gives the sum of terms in n-th group; A077282(n) gives the first term in n-th group; A077283(n) gives the last term in n-th group.
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EXAMPLE
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a(1)=9 because sum of first nine primes 2+...+23=100 is a square; a(2)=163 because sum of next 163 successive primes 29+...+1021=80089=283^2 is a square.
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MATHEMATICA
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f[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 1; c = d = 0; Do[s = 0; While[p = f[p]; c++; s = s + p; !IntegerQ[Sqrt[s]], ]; Print[c - d]; d = c, {n, 1, 50}]
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CROSSREFS
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Cf. A077281, A077282, A077283.
Sequence in context: A084874 A133681 A051232 this_sequence A041147 A041144 A086759
Adjacent sequences: A077277 A077278 A077279 this_sequence A077281 A077282 A077283
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KEYWORD
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nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), Nov 02 2002
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EXTENSIONS
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a(9) and a(10)>2500000 from Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 03 2002
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