A368531 Numbers whose binary indices are all powers of 3, where a binary index of n (row n of A048793) is any position of a 1 in its reversed binary expansion.

0, 1, 4, 5, 256, 257, 260, 261, 67108864, 67108865, 67108868, 67108869, 67109120, 67109121, 67109124, 67109125, 1208925819614629174706176, 1208925819614629174706177, 1208925819614629174706180, 1208925819614629174706181, 1208925819614629174706432

Offset

1,3

Comments

For powers of 2 instead of 3 we have A253317.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..256

Formula

a(3^n) = 2^(3^n - 1).

Example

The terms together with their binary expansions and binary indices begin:
         0:                           0 ~ {}
         1:                           1 ~ {1}
         4:                         100 ~ {3}
         5:                         101 ~ {1,3}
       256:                   100000000 ~ {9}
       257:                   100000001 ~ {1,9}
       260:                   100000100 ~ {3,9}
       261:                   100000101 ~ {1,3,9}
  67108864: 100000000000000000000000000 ~ {27}
  67108865: 100000000000000000000000001 ~ {1,27}
  67108868: 100000000000000000000000100 ~ {3,27}
  67108869: 100000000000000000000000101 ~ {1,3,27}
  67109120: 100000000000000000100000000 ~ {9,27}
  67109121: 100000000000000000100000001 ~ {1,9,27}
  67109124: 100000000000000000100000100 ~ {3,9,27}
  67109125: 100000000000000000100000101 ~ {1,3,9,27}

Mathematica

Select[Range[0, 10000], IntegerQ[Log[3, Times@@Join@@Position[Reverse[IntegerDigits[#, 2]], 1]]]&]
(* Second program *)
{0}~Join~Array[FromDigits[Reverse@ ReplacePart[ConstantArray[0, Max[#]], Map[# -> 1 &, #]], 2] &[3^(Position[Reverse@ IntegerDigits[#, 2], 1][[;; , 1]] - 1)] &, 255] (* Michael De Vlieger, Dec 29 2023 *)

Crossrefs

A000244 lists powers of 3.

A048793 lists binary indices, length A000120, sum A029931.

A070939 gives length of binary expansion.

A096111 gives product of binary indices.

Cf. A058891, A062050, A072639, A253317, A326031, A326675, A326702, A367912, A368183, A368109.

Sequence in context: A298224 A051152 A042181 * A042717 A304286 A134463

Adjacent sequences: A368528 A368529 A368530 * A368532 A368533 A368534

Keyword

nonn

Author

Gus Wiseman, Dec 29 2023

Status

approved