A104321 Smallest number m such that A104320(m)=n.
0, 5, 8, 18, 13, 26, 27, 23, 42, 25, 37, 58, 47, 46, 61, 67, 54, 71, 77, 73, 88, 99, 141, 100, 115, 114, 119, 117, 113, 112, 109, 135, 110, 127, 133, 136, 164, 162, 177, 186, 193, 195, 163, 189, 201, 196, 191, 199, 206, 188, 208, 200, 221, 266, 235, 234, 238, 280
Offset: 0
Keywords
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
Examples
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.
Programs
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PARI
a(n) = my(k=1); while (#select(x->(x==1), digits(2^k, 3)) != 2*n, k++); k; \\ Michel Marcus, Aug 17 2024
Formula
Conjecture: a(n) ~ 6*log_2(3)*n = 6*A020857*n.
Comments
Links
Crossrefs
Programs
PARI
a(n) = {my(k = 0); while (#select(x->(x==0), digits(2^k, 3)) != n, k++); k;} \\ Michel Marcus, Oct 19 2016