A264101 Numbers that can't be represented as the sum of two squares, two triangular numbers, or a square and a triangular number.
23, 33, 47, 62, 63, 86, 118, 134, 138, 143, 158, 167, 188, 195, 203, 204, 209, 223, 230, 243, 248, 275, 283, 294, 318, 323, 348, 368, 383, 385, 395, 398, 408, 411, 413, 418, 419, 426, 437, 440, 448, 454, 467, 473, 476, 489, 492, 503, 508, 518, 523, 558, 563, 566, 572, 608
Offset: 1
Keywords
Examples
Since 22 = 16+6, because 16 is a square and 6 is a triangular number, 22 is not a term. 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.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
N:= 1000: # for terms <= N S:= [seq(i^2,i=0..floor(sqrt(N)))]: nS:= nops(S): T:= [seq(i*(i+1)/2, i=0..floor(sqrt(2*N)))]: nT:= nops(T): sort(convert({$1..N} minus {seq(seq(S[i]+S[j], j=1..i),i=1..nS), seq(seq(S[i]+T[j],i=1..nS),j=1..nT), seq(seq(T[i]+T[j],j=1..i),i=1..nT)}, list)); # Robert Israel, May 19 2020 -
Mathematica
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 *)
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