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

Author

Tanya Khovanova, Jun 22 2009

Keywords

• base
• nonn

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.

Examples

			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).
		

Links

• T. Khovanova, Turning Numbers Inside Out [From _Tanya Khovanova_, Jul 07 2009]

Crossrefs

Cf. A161955, A161594, A161597.

Programs

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[ # ] == # &]

Extensions

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