A385157 Numbers k so that the binary expansion of 3^k starts with the binary expansion of k.

1, 2, 3, 9, 27, 65, 95, 123, 163, 303, 451, 597, 760, 1757, 2546, 2700, 7142, 25030, 25719, 25772, 49105, 61426, 90981, 107497, 194210, 659077, 6732590, 8513462, 9344030, 14549893, 32276115, 89912342, 181720904, 280120681, 437484689, 896754175, 10625891495, 30605576222

Offset

1,2

Links

Table of n, a(n) for n=1..38.

Example

9 is in the sequence as 3^9 is 100110011100011 in binary, and 9 is 1001.

Mathematica

q[k_] := k < Log[3, k+1] + (Floor[k*Log2[3]-Log2[k]])/Log2[3]; Select[Range[10^5], q] (* Amiram Eldar, Jun 20 2025 *)

Prog

(PARI) isok(k) = my(bk = binary(k), vb=Vec(binary(3^k), #bk)); vb == bk; \\ Michel Marcus, Jun 20 2025

Crossrefs

Cf. A000244, A004656.

Sequence in context: A178028 A045596 A057299 * A057296 A057248 A015960

Adjacent sequences: A385154 A385155 A385156 * A385158 A385159 A385160

Keyword

nonn,base

Author

Jayde S. Massmann, Jun 19 2025

Extensions

a(26) from Hugo Pfoertner, Jun 20 2025

a(27)-a(36) from Amiram Eldar, Jun 20 2025

a(37)-a(38) from Jinyuan Wang, Jun 27 2025

Status

approved