A235045 Fixed points of permutations A235041/A235042.

0, 1, 2, 3, 4, 6, 7, 8, 11, 12, 13, 14, 16, 19, 22, 24, 26, 28, 31, 32, 37, 38, 41, 44, 47, 48, 52, 56, 59, 61, 62, 64, 67, 73, 74, 76, 82, 88, 94, 96, 97, 103, 104, 109, 111, 112, 118, 122, 123, 124, 128, 131, 134, 135, 137, 146, 148, 152, 157, 159, 164, 167

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..2220

Example

In the following examples, X stands for the carryless multiplication of GF(2)[X] polynomials (A048720):
3 is a member, because it is in A091206, thus by definition fixed by A235041/A235042.
41 is a member for the same reason.
123 is a member, because 123 = 3*41, thus A235041(123) = A235041(3) X A235041(41) = 3 X 41 = A048720(3,41) = 123. That is, we happen to get the same result back as 3, '11' in binary, and 41, '101001' in binary, can be multiplied together to 123, '1111011' in binary, without producing any carries.
135 is a member, because 135 = 3*3*3*5, thus A235041(135) = A235041(3) X A235041(3) X A235041(3) X A235041(5) = 3 X 3 X 3 X 25 = 15 X 25 = 135.

Prog

(Scheme, with Antti Karttunen's IntSeq-library, two alternative definitions)
(define A235045 (FIXED-POINTS 1 0 A235041))
(define A235045v2 (FIXED-POINTS 1 0 A235042))

Crossrefs

The sequence differs from its subsequence A235032 for the first time at n=54, where a(54)=135, while A235032(54)=137.

A091206 gives the prime terms.

Cf. A235041, A235042.

Sequence in context: A175413 A192048 A235035 * A235032 A242925 A336444

Adjacent sequences: A235042 A235043 A235044 * A235046 A235047 A235048

Keyword

nonn

Author

Antti Karttunen, Jan 02 2014

Status

approved