cp's OEIS Frontend

A264101 Numbers that can't be represented as the sum of two squares, two triangular numbers, or a square and a triangular number.

%I A264101 #13 May 19 2020 16:56:13
%S A264101 23,33,47,62,63,86,118,134,138,143,158,167,188,195,203,204,209,223,
%T A264101 230,243,248,275,283,294,318,323,348,368,383,385,395,398,408,411,413,
%U A264101 418,419,426,437,440,448,454,467,473,476,489,492,503,508,518,523,558,563,566,572,608
%N A264101 Numbers that can't be represented as the sum of two squares, two triangular numbers, or a square and a triangular number.
%C A264101 Intersection of A014134, A020757, A022544.
%H A264101 Robert Israel, <a href="/A264101/b264101.txt">Table of n, a(n) for n = 1..10000</a>
%e A264101 Since 22 = 16+6, because 16 is a square and 6 is a triangular number, 22 is not a term.
%e A264101 23 is a term because there is no representation as S+T or S1+S2 or T1+T2, where S, S1, S2 are squares, and T, T1, T2 are triangular numbers.
%p A264101 N:= 1000: # for terms <= N
%p A264101 S:= [seq(i^2,i=0..floor(sqrt(N)))]: nS:= nops(S):
%p A264101 T:= [seq(i*(i+1)/2, i=0..floor(sqrt(2*N)))]: nT:= nops(T):
%p A264101 sort(convert({$1..N} minus {seq(seq(S[i]+S[j], j=1..i),i=1..nS),
%p A264101 seq(seq(S[i]+T[j],i=1..nS),j=1..nT),
%p A264101 seq(seq(T[i]+T[j],j=1..i),i=1..nT)}, list)); # _Robert Israel_, May 19 2020
%t A264101 mx = 610; Complement[ Range@ mx, Union@ Flatten@ Table[{i^2 + j^2, i(i + 1)/2 + j^2, i(i + 1)/2 + j(j + 1)/2}, {i, 0, Sqrt[2 mx]}, {j, 0, Sqrt[2 mx]}]] (* _Robert G. Wilson v_, Nov 29 2015 *)
%Y A264101 Cf. A000217, A000290, A014134, A020757, A022544, A264118.
%K A264101 nonn
%O A264101 1,1
%A A264101 _Alex Ratushnyak_, Nov 03 2015