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Numbers that are not the difference between any triangular number and the largest square that does not exceed it.
2

%I #9 Oct 31 2019 01:25:14

%S 4,7,8,13,16,18,22,23,25,26,31,33,34,37,38,40,43,47,48,49,52,58,59,60,

%T 61,63,64,67,68,70,73,76,79,81,83,85,86,88,92,93,94,97,98,99,102,103,

%U 106,108,112,113,114,115,118,121,123,124,125,130,133,134,138

%N Numbers that are not the difference between any triangular number and the largest square that does not exceed it.

%e For any triangular number t, let f(t) = t - floor(sqrt(t))^2.

%e 0 is not a term: for each term t in A001110, f(t) = 0.

%e 1 is not a term: for each term t > 1 in A164055, f(t) = 1.

%e 2 is not a term: for each term t in A214838, f(t) = 2.

%e 3 is not a term: for each term t > 3 in A328791, f(t) = 3.

%e 4 is a term, however: there exists no triangular number t such that f(t) = 4.

%Y The complement of A230044.

%Y Cf. A001110, A064784, A164055, A214838, A328791.

%K nonn

%O 1,1

%A _Jon E. Schoenfield_, Oct 27 2019