A231928 - OEIS

A231928

Working in base 7: 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.

%I #7 Nov 16 2013 14:16:05

%S 0,11,1,10,100,12,2,20,101,22,3,13,31,103,30,110,33,4,14,41,104,40,

%T 114,24,42,112,21,102,120,201,210,1000,105,15,5,25,52,115,35,53,113,

%U 23,32,121,26,6,16,61,106,60,116,36,63,131,34,43,134,143,314,341,413,431,1003

%N Working in base 7: 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 7 - see the Comments in A228407 for the proof.

%t a[0] = 0; a[n_] := a[n] = Block[{k = 1, idm = IntegerDigits[ a[n - 1], 7], t = a@# & /@ Range[n - 1]}, Label[ start]; While[ MemberQ[t, k], k++]; While[ Select[ Permutations[ Join[ idm, IntegerDigits[k, 7]]], #[[1]] != 0 && # == Reverse@# &] == {}, k++; Goto[ start]]; k]; s = Array[a, 60, 0]; FromDigits@# & /@ IntegerDigits[s, 7]

%Y Cf. A230891, A231920, A231922, A231924, A231926, A231930, A231932, A228407, A231929.

%K nonn,base,easy

%O 0,2

%A _N. J. A. Sloane_ and _Robert G. Wilson v_, Nov 15 2013