OFFSET
1,1
COMMENTS
Sun has proved that the a(n) are those positive triangular numbers A000217(m) for which all the prime divisors of 2m+1 are congruent to 1 (mod 4).
LINKS
Zhi-Wei Sun, Mixed sums of squares and triangular numbers, Acta Arith. 127, (2007), No. 2, pp. 103-113.
EXAMPLE
The fifth integer that cannot be partitioned into a sum of an odd square, an even square and a triangular number is 105. Hence a(5)=105.
MATHEMATICA
Test[n_] := Module[{x, y, z}, FindInstance[(2x+1)^2 + (2 y)^2 + z (z+1)/2 == n && 0 <= x <= n && 0 <= y <= n && 0 <= z <= n, {x, y, z}, Integers]]; Select[Range[1000], Length[Test[#]] == 0 &]
PROG
(PARI) is_A191763(N)=issquare(N*8+1, &N)&N%4==1&vecsort(factor(N)[, 1]~%4, , 8)==[1] \\ M. F. Hasler, Jun 22 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ant King, Jun 22 2011
STATUS
approved