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%I #7 Nov 16 2013 14:15:28
%S 0,11,1,10,100,12,2,20,101,22,3,13,31,103,30,110,33,4,14,41,104,40,
%T 114,24,42,112,21,102,120,201,210,1000,111,44,113,23,32,121,200,211,
%U 222,233,244,323,332,424,442,1001,122,133,144,212,221,313,331,414,441,1002,123
%N Working in base 5: a(0)=0, thereafter a(n+1) is the smallest number not already in the sequence such that the bits of a(n) and a(n+1) together can be rearranged to form a palindrome.
%C This is a permutation of the nonnegative integers in base 5 - see the Comments in A228407 for the proof.
%t a[0] = 0; a[n_] := a[n] = Block[{k = 1, idm = IntegerDigits[ a[n - 1], 5], t = a@# & /@ Range[n - 1]}, Label[ start]; While[ MemberQ[t, k], k++]; While[ Select[ Permutations[ Join[ idm, IntegerDigits[k, 5]]], #[[1]] != 0 && # == Reverse@# &] == {}, k++; Goto[ start]]; k]; s = Array[a, 60, 0]; FromDigits@# & /@ IntegerDigits[s, 5]
%Y Cf. A230891, A231920, A231922, A231926, A231928, A231930, A231932, A228407, A231925.
%K nonn,base,easy
%O 0,2
%A _N. J. A. Sloane_ and _Robert G. Wilson v_, Nov 15 2013