A332802 a(n) is the smallest q such that the number of nonnegative k <= q, possessing the property that k + k*q - q is a square, is equal to 2^n.
0, 2, 7, 23, 119, 839, 9239, 120119, 2042039, 38798759, 892371479, 25878772919, 802241960519, 29682952539239, 1217001054108839, 52331045326680119, 2459559130353965639, 130356633908760178919, 7691041400616850556279, 469153525437627883933079, 31433286204321068223516379
Offset: 0
Keywords
Examples
a(0) = 0 because 2^0 = 1 solution is 0 (where k=0). a(1) = 2 because 2^1 = 2 solutions are 1 (1) and 4 (2). a(2) = 7 because 2^2 = 4 solutions are 1 (1), 9 (2), 25 (4), 49 (7). a(3) = 23 because 2^3 = 8 solutions are 1 (1), 25 (2), 49 (3), 121 (6), 169 (8), 289 (13), 361 (16), 529 (23). a(4) = 119 because 2^4 = 16 solutions are 1 (1), 121 (2), 361 (4), 841 (8), 961 (9), 1681 (15), 2401 (21), 3481 (30), 3721 (32), 5041 (43), 6241 (53), 7921 (67), 8281 (70), 10201 (86), 11881 (100), 14161 (119).
Programs
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PARI
a(n) = {my(q=0); while (sum(k=0, q, issquare(k + k*q - q)) != 2^n, q++); q;} \\ Michel Marcus, Feb 25 2020
Formula
a(n) = A102476(n) - 1. - Jinyuan Wang, Feb 25 2020
Extensions
a(7) from Michel Marcus, Feb 25 2020
More terms from Jinyuan Wang, Feb 25 2020