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

Author

Jayde S. Massmann, Jun 19 2025

Keywords

• nonn
• base

Examples

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

Crossrefs

Cf. A000244, A004656.

Programs

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 *)

PARI

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