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%I #5 Feb 22 2019 01:45:50
%S 0,2,3,4,5,6,7,8,9,10,2,4,6,8,10,3,5,7,9,11,2,5,8,11,3,6,9,12,3,7,10,
%T 4,7,11,4,8,12,4,9,13,4,10,5,9,14,5,10,6,10,7,12,5,11,5,12,6,11,6,12,
%U 7,13,5,13,6,13,7,14,6,14,7,15,6,15,7,16,7,17,8,13,8,14,8,15,8,16,8,17,9,15
%N "Walking base" sequence: the number becomes the least base in which it could be read, once; written in base 10.
%C A "base" sequence visiting all the bases but nevertheless written here in base 10.
%C The number a(n) do not become its value in the new base, but becomes the base itself. So each term has a double status according to its preceding or following neighbor: regarding a(n-1), a(n) is a *base* (the least one not used so far) in which it is possible to read a(n-1); and regarding a(n+1), a(n) is a *number* to be read in the base expressed by a(n+1).
%C The first break, specific of this sequence written in base 10, occurs after a(9)=10. If, following the same principle, one build another sequence written, say in base 8, the beginning would be: 0,2,3,4,5,6,7,10,2,4... the first break occurring after a(7) instead of a(9). The inclusion of the unary base would lead to a different sequence since after the first occurrence of 11 would come 1 and not 2.
%C The word "walking base" refers to the "walking bass", a certain style of accompaniment in baroque music or jazz bass playing, in which the player, using a bass line composed of nonsyncopated notes of equal value, moves in stepwise motion to successive chord roots or notes, sometimes using passing notes.
%H <a href="http://www.projects.ex.ac.uk/trol/scol/calnumba.htm">The number base calculator</a>,
%e Examples: The beginning is 0,2,3 but could also be 1,2,3.
%e a(0)=0. Now the least base in which 0 has a meaning is the binary base, so next term, a(1)=2.
%e The least base in which 2 makes sense is 3, so next term, a(2)=3.
%e The least base in which "10" makes sense is not base 11 but base 2, so next term, a(10)=2 (although 2 was used to read 0, it has not yet been used to read "10").
%e The least base in which this second 2 makes sense now is not 3 (because 3 has already been used to read a(1)=2), but 4, so next term a(11)=4.
%e a(101)=10: the least base not used so far to read "10" is base 10, so a(102)=10; then a(103)=11 (and although the value a(102)="10" in base 11 should be written "A", which is impossible in the OEIS, this does not affect the next term a(103); anyway, this walking base is written all along in base 10, so a(102)=10).
%K base,nonn
%O 0,2
%A _Alexandre Wajnberg_, Feb 20 2006
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