A111302 Define a(1)=1. Thereafter a(n) is the smallest positive integer with the property that a(n)^2 cannot be created by summing the squares of at most n values chosen among the previous terms (with repeats allowed).

1, 2, 4, 9, 12, 16, 27, 49, 69, 118, 187, 305, 503, 829, 1590, 2529, 4173, 7189, 13771, 22854, 43460, 57549, 135271, 222070, 426775, 724479, 1246636, 2158543, 3713979, 6063658, 11725956, 19627746

Offset

1,2

Comments

No more terms < 22155000. - David Wasserman, Jan 09 2009

Links

Table of n, a(n) for n=1..32.

Example

a(3) <> 3 because we can write 3^2 = a(2)^2 + a(2)^2 + a(1)^2 by using not more than 3 terms.
But it is impossible to write 4^2 as the sum of at most three squares of the previous elements, thus a(3)=4.

Prog

(PARI) canMake(n, v, i, left) = local(c); if (i == 0, return(n <= left)); c = v[i]; if (n > left*c, return(0)); if (!(n%c), return(1)); forstep (j = n\c, 0, -1, if (canMake(n - j*c, v, i - 1, left - j), return(1))); 0;
v = vector(60); x = 2; for (m = 2, 61, while (canMake(x^2, v, m - 2, m), x++); v[m - 1] = x^2; print1(x, ", "); x++); \\ David Wasserman, Jan 09 2009

Crossrefs

Sequence in context: A341239 A088901 A283147 * A241200 A092530 A154891

Adjacent sequences: A111299 A111300 A111301 * A111303 A111304 A111305

Keyword

nonn,hard

Author

Stefan Steinerberger, Nov 02 2005

Extensions

More terms from David Wasserman, Jan 09 2009

Status

approved