A219659 - OEIS

%I #9 Nov 26 2012 00:01:45

%S 0,1,0,2,1,0,3,1,0,4,2,1,0,5,2,1,0,6,5,2,1,0,7,5,2,1,0,8,6,5,2,1,0,9,

%T 6,5,2,1,0,10,7,5,2,1,0,11,7,5,2,1,0,12,10,7,5,2,1,0,13,10,7,5,2,1,0,

%U 14,11,7,5,2,1,0,15,11,7,5,2,1,0,16,12,10,7,5,2,1,0

%N Irregular table where row n (n >= 0) starts with n, the next term is A219651(n), and the successive terms are obtained by repeatedly subtracting the sum of digits in the previous term's factorial expansion, until zero is reached, after which the next row starts with one larger n.

%C Rows converge towards A219666 (reversed).

%C See A007623 for the Factorial number system representation.

%H A. Karttunen, <a href="/A219659/b219659.txt">Rows 0..120, flattened</a>

%o (Scheme with _Antti Karttunen_'s Intseq-library):

%o (definec (A219659 n) (cond ((< n 2) n) ((not (zero? (A219659 (- n 1)))) (A219651 (A219659 (- n 1)))) (else (+ 1 (A219659 (+ 1 (Aux_for_219659 (- n 1))))))))

%o (define Aux_for_219659 (compose-funs A219657 -1+ (LEAST-GTE-I 0 0 A219657))) ;; Gives the position of previous zero.

%Y Cf. A007623, A034968, A219651, A219657. Analogous sequence for binary system: A218254, for Zeckendorf expansion: A219649.

%K nonn,tabf

%O 0,4

%A _Antti Karttunen_, Nov 25 2012