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

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = A102476(n) - 1. - Jinyuan Wang, Feb 25 2020

Example

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 (60, 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).

Prog

(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

Crossrefs

Cf. A000290, A060594, A102476, A332761.

Sequence in context: A049021 A345871 A375130 * A002494 A032264 A139522

Adjacent sequences: A332799 A332800 A332801 * A332803 A332804 A332805

Keyword

nonn

Author

Juri-Stepan Gerasimov, Feb 24 2020

Extensions

a(7) from Michel Marcus, Feb 25 2020

More terms from Jinyuan Wang, Feb 25 2020

Status

approved