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A161957
Fixed points of A161955.
0
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.
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
KEYWORD
base,nonn
AUTHOR
Tanya Khovanova, Jun 22 2009
EXTENSIONS
Comments condensed by R. J. Mathar, Aug 14 2009
STATUS
approved