A379340
Integers m such that m^2 is the sum of two or more squares of consecutive integers in more than one way.
Original entry on oeis.org
70, 105, 143, 195, 2849, 3854, 5681, 8075, 143737, 144157, 208395, 939356, 1226670, 2259257, 2656724, 2741046, 4598528, 6555549, 7832413, 11818136, 19751043, 32938290, 429323037, 807759678, 1375704770, 1656510196, 1981351834
Offset: 1
105^2 = (-19)^2 + (-18)^2 + ... + 29^2 = (-21)^2 + (-20)^2 + ... + 28^2.
143^2 = 38^2 + 39^2 + ... + 48^2 = 7^2 + 8^2 + ... + 39^2.
2259257^2 = 26181^2 + 26182^2 + ... + 32158^2 = 9401^2 + 9402^2 + ... + 25273^2.
A218214
Number of primes up to 10^n representable as sums of consecutive squares.
Original entry on oeis.org
1, 5, 18, 48, 117, 304, 823, 2224, 6113, 16974, 48614, 139349
Offset: 1
a(1) = 1 because only one prime less than 10 can be represented as a sum of consecutive squares, namely 5 = 1^2 + 2^2.
a(2) = 5 because there are five primes less than 100 representable as a sum of consecutive squares: the aforementioned 5, as well as 13 = 2^2 + 3^2, 29 = 2^2 + 3^2 + 4^2, 41 = 4^2 + 5^2 and 61 = 5^2 + 6^2.
Cf.
A027861,
A027862,
A027863,
A027864,
A027866,
A027867,
A163251,
A174069,
A218208,
A218210,
A218212,
A218213.
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nn = 8; nMax = 10^nn; t = Table[0, {nn}]; Do[k = n; s = 0; While[s = s + k^2; s <= nMax, If[PrimeQ[s], t[[Ceiling[Log[10, s]]]]++]; k++], {n, Sqrt[nMax]}]; Accumulate[t] (* T. D. Noe, Oct 23 2012 *)
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