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%I #10 Mar 25 2015 01:21:18
%S 9,163,155,232,12,4599,1474,9156,138429
%N Sum of next a(n) successive primes is a square.
%C 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-???}, ...
%C 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.
%C a(10) > 2500000. - _Robert G. Wilson v_, Nov 03 2002
%e 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.
%t 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}]
%Y Cf. A077281, A077282, A077283.
%K nonn
%O 1,1
%A _Zak Seidov_, Nov 02 2002
%E a(9) from _Robert G. Wilson v_, Nov 03 2002
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