A077280 Sum of next a(n) successive primes is a square.

9, 163, 155, 232, 12, 4599, 1474, 9156, 138429

Offset

1,1

Comments

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.

a(10) > 2500000. - Robert G. Wilson v, Nov 03 2002

Links

Table of n, a(n) for n=1..9.

Example

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.

Mathematica

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}]

Crossrefs

Cf. A077281, A077282, A077283.

Sequence in context: A051232 A362900 A157574 * A297436 A041147 A041144

Adjacent sequences: A077277 A077278 A077279 * A077281 A077282 A077283

Keyword

nonn

Author

Zak Seidov, Nov 02 2002

Extensions

a(9) from Robert G. Wilson v, Nov 03 2002

Status

approved