A163251 Primes that are sum of (at least two) consecutive squares.

5, 13, 29, 41, 61, 113, 139, 149, 181, 199, 271, 313, 421, 509, 613, 677, 761, 811, 1013, 1201, 1279, 1301, 1459, 1741, 1861, 1877, 2113, 2381, 2521, 2539, 2791, 3121, 3331, 3613, 3677, 3919, 4231, 4513, 5101, 7159, 7321, 8011, 8429, 8581, 9661, 9749, 9859

Offset: 1

Author

Gaurav Kumar, Jul 23 2009

Keywords

• nonn

Comments

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

Examples

			5 = 1^2 + 2^2.
13 = 2^2 + 3^2.
29 = 2^2 + 3^2 + 4^2.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

A027862 is a subsequence.

Subsequence of A174069.

Programs

Mathematica

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 *)
Select[Union[Flatten[Table[Total/@Partition[Range[100]^2,n,1],{n,2,10}]]],PrimeQ] (* Harvey P. Dale, Mar 12 2015 *)

Extensions

Offset corrected by Donovan Johnson, Nov 05 2012