A161730 -id:A161730 - cp's OEIS frontend

A161732 Fixed points of the TITO operation (A161594) that are also composite palindromes.

4, 6, 8, 9, 22, 33, 44, 55, 66, 77, 88, 99, 121, 202, 242, 252, 262, 303, 343, 363, 393, 404, 484, 505, 525, 606, 616, 626, 686, 707, 808, 909, 939, 1111, 1331, 1441, 1661, 1991, 2112, 2222, 2662, 2772, 2882, 3333, 3443, 3773, 3883, 3993, 4224, 4444, 5445

Offset: 1

Tanya Khovanova, Jun 17 2009

This sequence is a proper superset of A046351 (palindromic composite numbers with only palindromic prime factors). The smallest number that doesn't belong to A046351 is 72927. The numbers that are in this sequence and are not in A046351 are given in A161730.

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

Cf. A161594, A161597, A161598, A161600, A046351

reversepower[{n_, k_}] := FromDigits[Reverse[IntegerDigits[n]]]^k f[n_] := FromDigits[ Reverse[IntegerDigits[Times @@ Map[reversepower, FactorInteger[n]]]]] rev[n_] := FromDigits[Reverse[IntegerDigits[n]]] Select[Range[10000], f[ # ] == # && rev[ # ] == # && ! PrimeQ[ # ] &]

Edited by N. J. A. Sloane, Jun 23 2009

A162151 Numbers n such that m=TITO(n)>n and TITO(m)=n, where TITO() = A161594().

Original entry on oeis.org

12, 18, 24, 27, 36, 45, 48, 132, 144, 156, 198, 264, 276, 288, 291, 297, 372, 375, 396, 405, 492, 495, 528, 576, 1089, 1212, 1236, 1287, 1356, 1359, 1452, 1572, 1584, 1629, 1683, 1728, 1812, 1818, 2002, 2067, 2079, 2178, 2304, 2424, 2532, 2676, 2721, 2727

Offset: 1

Zak Seidov, Jun 26 2009

Or, numbers that end in two-cycles under TITO operation.

			For smaller n's, m is a reversal of n, but for larger n's, there are other cases as well:{12,21},{18,81},{24,42},{27,72},...,{291,732},...,{372,651}, etc.

Zak Seidov, 141 pairs {n,m} for n<30000
T. Khovanova, Turning Numbers Inside Out [From _Tanya Khovanova_, Jul 07 2009]

Cf. A161594, A161597, A161598, A161600, A161730, A161732.

m=A161594(n)>n, and A161594(m)=n.

cp's OEIS Frontend

A161732 Fixed points of the TITO operation (A161594) that are also composite palindromes.

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