%I #16 Feb 20 2023 05:17:31
%S 3970902,39022919,102132857,110468517,368495972,391099413,395147912,
%T 421129348,452808398,776218485,1005771844,1485470432,3038310485,
%U 3263773338,3485976107,3640901241,3758331463,3784200441,3944795435
%N Positive numbers that are not the sum of a triangular number, a square and a Fibonacci number.
%C Prompted by a conjecture of _Zhi-Wei Sun_ (now known not to be true) that every number can be written in the stated form.
%C A number n = x^2 + y*(y+1)/2 + F_m if and only if 8*n+1 = 8*x^2 + (2*y+1)^2 + 8*F_m, if and only if 8*n + 1 - 8*F_m = 8*x^2 + (2*y+1)^2 for some m >= 0. Now if M == 1 (mod 8) (e.g. M = 8*n + 1 -8*F_m), then M = 8*x^2 + (2*y+1)^2 if and only if the exact prime-power exponent of each prime p == 5 or 7 (mod 8) which divides M is even.
%C a(10) was found by _D. S. McNeil_ in 12/2008.
%H Donovan Johnson, <a href="/A144642/b144642.txt">Table of n, a(n) for n = 1..101</a> (terms < 4*10^10)
%H Zhi-Wei SUN, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;2446667f.0812">Posting to Number Theory List, Dec 21 2008</a>
%Y See A115171 for another version.
%K nonn
%O 1,1
%A Kurt Foster (drsardonicus(AT)earthlink.net), Jan 25 2009
%E Definition corrected and a(3)-a(19) from _Donovan Johnson_, Oct 24 2009