A375472 Least k such that the ternary representation of 2^k has exactly 2*n 1's, or -1 if no such k exists.

1, 2, 8, 14, 24, 26, 42, 45, 50, 53, 70, 74, 96, 76, 124, 98, 116, 121, 143, 141, 179, 150, 187, 181, 192, 215, 209, 233, 220, 257, 245, 264, 243, 278, 260, 310, 297, 303, 315, 339, 329, 387, 341, 357, 354, 366, 403, 420, 350, 400, 411, 415, 474, 455, 466, 442

Offset

0,2

Links

Table of n, a(n) for n=0..55.

Formula

Conjecture: a(n) ~ 6*log_2(3)*n = 6*A020857*n.

Example

For n = 3, the smallest power of 2 with exactly 2*3 = 6 1's in its ternary representation is 2^14 = 211110211_3, so a(3) = 14.

Prog

(PARI) a(n) = my(k=1); while (#select(x->(x==1), digits(2^k, 3)) != 2*n, k++); k; \\ Michel Marcus, Aug 17 2024

Crossrefs

Cf. A020857, A060035, A104321, A365214.

Sequence in context: A248057 A121055 A344161 * A107072 A120413 A161156

Adjacent sequences: A375468 A375469 A375471 * A375473 A375474 A375475

Keyword

nonn,base

Author

Pontus von Brömssen, Aug 17 2024

Status

approved