cp's OEIS Frontend

A097563 Least integer that can be written as a sum of zero or more distinct squares in exactly n ways, or -1 if no such number exists.

%I A097563 #10 Sep 05 2015 05:26:17
%S A097563 2,0,25,50,65,94,90,110,155,126,191,170,186,174,190,211,195,226,210,
%T A097563 231,234,235,332,255,283,259,274,275,270,323,310,286,306,299,330,381,
%U A097563 295,347,334,319,315,331,405,339,335,364,359,351,367,387,371,370,404,438
%N A097563 Least integer that can be written as a sum of zero or more distinct squares in exactly n ways, or -1 if no such number exists.
%C A097563 a(n) = -1 for almost all n. Conjecture: for n > 34189857569982621, this sequence is the integers > 37163, in order, interspersed with -1s. - _Charles R Greathouse IV_, Sep 04 2015
%H A097563 Charles R Greathouse IV, <a href="/A097563/b097563.txt">Table of n, a(n) for n = 0..10000</a>
%e A097563 a(4) = 65 because we can write 65 as a sum of distinct squares in four ways: 65 = 8^2 + 1^2 = 7^2 + 4^2 = 6^2 + 5^2 + 2^2 = 6^2 + 4^2 + 3^2 + 2^2 and we cannot do this with any smaller integer.
%e A097563 a(0) = 2 because we cannot write 2 as a sum of distinct squares and it is the smallest number with this property.
%p A097563 gf := product(1+x^F(k), k=1..31); ser := series(gf, x=0, 1001); S := [seq(coeff(ser,x^(1*i)),i=1..1000)]; A := proc(i); x := 0; for j from 1 to nops(a) while x = 0 do > if a[j] = i then x := 1; fi; od; j-1; end; seq(A(n), n=1..67);
%Y A097563 First occurrence of n in A033461; see also A001422 (0 ways) and A003995 (1 or more ways).
%K A097563 easy,sign
%O A097563 0,1
%A A097563 Isabel C. Lugo (izzycat(AT)gmail.com), Aug 27 2004
%E A097563 Edited by _Ray Chandler_, Sep 01 2004