|
%I #10 Jan 16 2014 15:04:55
%S 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,
%T 48,52,56,59,61,62,64,67,73,74,76,82,88,94,96,97,103,104,109,111,112,
%U 118,122,123,124,128,131,134,135,137,146,148,152,157,159,164,167
%N Fixed points of permutations A235041/A235042.
%H Antti Karttunen, <a href="/A235045/b235045.txt">Table of n, a(n) for n = 1..2220</a>
%e In the following examples, X stands for the carryless multiplication of GF(2)[X] polynomials (A048720):
%e 3 is a member, because it is in A091206, thus by definition fixed by A235041/A235042.
%e 41 is a member for the same reason.
%e 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.
%e 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.
%o (Scheme, with _Antti Karttunen_'s IntSeq-library, two alternative definitions)
%o (define A235045 (FIXED-POINTS 1 0 A235041))
%o (define A235045v2 (FIXED-POINTS 1 0 A235042))
%Y The sequence differs from its subsequence A235032 for the first time at n=54, where a(54)=135, while A235032(54)=137.
%Y A091206 gives the prime terms.
%Y Cf. A235041, A235042.
%K nonn
%O 1,3
%A _Antti Karttunen_, Jan 02 2014
|
