A161957 Fixed points of A161955.

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 27, 29, 31, 37, 41, 43, 45, 47, 51, 53, 59, 61, 63, 67, 71, 73, 79, 83, 85, 89, 93, 95, 97, 101, 103, 107, 109, 111, 113, 119, 123, 127, 131, 137, 139, 149, 151, 153, 157, 163, 167, 173, 179, 181, 187, 189, 191, 193, 197, 199

Offset

1,2

Comments

Fixed points of the TITO2 operation (the TITO operation in binary): numbers a(n) such that A161955(a(n)) = a(n).

All numbers in the sequence are odd. All odd primes A065091 belong to the sequence.

Links

Table of n, a(n) for n=1..62.

T. Khovanova, Turning Numbers Inside Out [From Tanya Khovanova, Jul 07 2009]

Example

95 is in this sequence because 95 = 5*19. Prime factors in binary are: 101 and 10011.
Reversing them we get 101 and 11001. The product of the last two numbers is 1111101, which is
the reverse of the binary representation of 95 (1011111).

Mathematica

reverseBinPower[{n_, k_}] := FromDigits[Reverse[IntegerDigits[n, 2]], 2]^k fBin[n_] := FromDigits[ Reverse[IntegerDigits[ Times @@ Map[reverseBinPower, FactorInteger[n]], 2]], 2] Select[Range[300], fBin[ # ] == # &]

Crossrefs

Cf. A161955, A161594, A161597.

Sequence in context: A353076 A033039 A322660 * A082720 A033037 A246413

Adjacent sequences: A161954 A161955 A161956 * A161958 A161959 A161960

Keyword

base,nonn

Author

Tanya Khovanova, Jun 22 2009

Extensions

Comments condensed by R. J. Mathar, Aug 14 2009

Status

approved