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A264101
Numbers that can't be represented as the sum of two squares, two triangular numbers, or a square and a triangular number.
2
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
1,1
COMMENTS
Intersection of A014134, A020757, A022544.
LINKS
EXAMPLE
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.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alex Ratushnyak, Nov 03 2015
STATUS
approved