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%I #33 May 01 2015 16:00:38
%S 5,13,29,41,61,113,139,149,181,199,271,313,421,509,613,677,761,811,
%T 1013,1201,1279,1301,1459,1741,1861,1877,2113,2381,2521,2539,2791,
%U 3121,3331,3613,3677,3919,4231,4513,5101,7159,7321,8011,8429,8581,9661,9749,9859
%N Primes that are sum of (at least two) consecutive squares.
%C Let S(n,k) = (n+1)^2 + (n+2)^2 +... + (n+k)^2, n>=0, k>=2. S(n,k) is always composite for k=4 (2 | S), k=5 (5 | S), and k >= 7 (see A256503). So a(n) is the sum of 2, 3, or 6 consecutive squares. The smallest a(n) that cannot be written as a sum of fewer than 6 consecutive squares is a(7)=139. - _Vladimir Shevelev_, Apr 08 2015
%H Donovan Johnson, <a href="/A163251/b163251.txt">Table of n, a(n) for n = 1..1000</a>
%e 5 = 1^2 + 2^2.
%e 13 = 2^2 + 3^2.
%e 29 = 2^2 + 3^2 + 4^2.
%t lst = {}; Do[p = m^2; Do[p += n^2; If[PrimeQ[p] && p <= 101701, AppendTo[lst, p]], {n, m + 1, 6!, 1}], {m, 6!}]; Take[Union@lst, 5! (* _Vladimir Joseph Stephan Orlovsky_, Sep 15 2009 *)
%t Select[Union[Flatten[Table[Total/@Partition[Range[100]^2,n,1],{n,2,10}]]],PrimeQ] (* _Harvey P. Dale_, Mar 12 2015 *)
%Y A027862 is a subsequence.
%Y Subsequence of A174069.
%K nonn
%O 1,1
%A _Gaurav Kumar_, Jul 23 2009
%E Offset corrected by _Donovan Johnson_, Nov 05 2012