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 A232179 Least k >= 0 such that n^2 + triangular(k) is a triangular number. 4
 0, 0, 3, 1, 15, 2, 0, 3, 63, 4, 8, 5, 11, 6, 20, 3, 255, 8, 1, 9, 3, 10, 38, 11, 59, 12, 45, 13, 8, 14, 2, 15, 1023, 16, 59, 0, 24, 18, 66, 19, 51, 20, 3, 21, 44, 10, 80, 23, 251, 24, 42, 25, 68, 26, 4, 27, 39, 28, 101, 29, 10, 30, 108, 8, 4095, 32, 5, 33, 128 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Triangular(k) = k*(k+1)/2. LINKS Chai Wah Wu, Table of n, a(n) for n = 0..10000 FORMULA a(A001109(n)) = 0. MATHEMATICA TriangularQ[n_] := IntegerQ[Sqrt[1 + 8*n]]; Table[k = 0; While[! TriangularQ[n^2 + k*(k + 1)/2], k++]; k, {n, 0, 68}] (* T. D. Noe, Nov 21 2013 *) PROG (Python) from __future__ import division from sympy import divisors def A232179(n):     if n == 0:         return 0     t = 2*n**2     ds = divisors(t)     for i in range(len(ds)//2-1, -1, -1):         x = ds[i]         y = t//x         a, b = divmod(y-x, 2)         if b:             return a     return -1 # Chai Wah Wu, Sep 12 2017 (PARI) a(n) = {my(k = 0); while (! ispolygonal(n^2 + k*(k+1)/2, 3), k++); k; } \\ Michel Marcus, Sep 15 2017 CROSSREFS Cf. A000217, A000290, A001109. Cf. A082183 (least k>0 such that triangular(n) + triangular(k) is a triangular number). Cf. A232177 (least k>0 such that triangular(n) + triangular(k) is a square). Cf. A232176 (least k>0 such that n^2 + triangular(k) is a square). Cf. A101157 (least k>0 such that triangular(n) + k^2 is a triangular number). Cf. A232178 (least k>=0 such that triangular(n) + k^2 is a square). Sequence in context: A318142 A176727 A080924 * A128042 A108083 A163239 Adjacent sequences:  A232176 A232177 A232178 * A232180 A232181 A232182 KEYWORD nonn AUTHOR Alex Ratushnyak, Nov 20 2013 STATUS approved

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Last modified October 19 22:05 EDT 2021. Contains 348095 sequences. (Running on oeis4.)