This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A266123 #9 Dec 25 2015 21:05:28 %S A266123 0,0,1,1,1,1,2,2,3,3,3,3,2,2,3,3,3,3,4,4,5,5,5,5,6,6,7,7,7,7,8,8,9,9, %T A266123 9,9,8,8,9,9,9,9,10,10,11,11,11,11,6,6,7,7,7,7,8,8,9,9,9,9,8,8,9,9,9, %U A266123 9,10,10,11,11,11,11,12,12,13,13,13,13,14,14,15,15,15,15,14,14,15,15,15,15,16,16,17,17,17,17,18 %N A266123 Decrement by 1 all digits > 1 in factorial base representation of n and then shift it one digit right. %H A266123 Antti Karttunen, <a href="/A266123/b266123.txt">Table of n, a(n) for n = 0..10080</a> %H A266123 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a> %e A266123 n A007623(n) [subtract 1 from digits > 1 a(n) %e A266123 [in factorial then shift one digit right] [reinterpret %e A266123 base] in decimal] %e A266123 0 0 -> 0 = 0 %e A266123 1 1 -> 0 = 0 %e A266123 2 10 -> 1 = 1 %e A266123 3 11 -> 1 = 1 %e A266123 4 20 -> 1 = 1 %e A266123 5 21 -> 1 = 1 %e A266123 6 100 -> 10 = 2 %e A266123 7 101 -> 10 = 2 %e A266123 8 110 -> 11 = 3 %e A266123 9 111 -> 11 = 3 %e A266123 10 120 -> 11 = 3 %e A266123 11 121 -> 11 = 3 %e A266123 12 200 -> 10 = 2 %e A266123 13 201 -> 10 = 2 %e A266123 14 210 -> 11 = 3 %e A266123 15 211 -> 11 = 3 %e A266123 16 220 -> 11 = 3 %e A266123 17 221 -> 11 = 3 %e A266123 18 300 -> 20 = 4 %o A266123 (MIT/GNU Scheme) %o A266123 (define (A266123 n) (let loop ((n n) (z 0) (i 2) (f 0)) (cond ((zero? n) z) (else (let ((d (remainder n i))) (loop (quotient n i) (+ z (* f (- d (if (<= d 1) 0 1)))) (+ 1 i) (if (zero? f) 1 (* f (- i 1))))))))) %Y A266123 Cf. A007623, A257684, A266193. %K A266123 nonn,base %O A266123 0,7 %A A266123 _Antti Karttunen_, Dec 23 2015