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 A276090 #11 Aug 21 2016 21:37:18
%S A276090 0,1,0,1,0,1,2,3,2,3,2,3,4,5,4,5,4,5,6,7,6,7,6,7,0,1,0,1,0,1,2,3,2,3,
%T A276090 2,3,4,5,4,5,4,5,6,7,6,7,6,7,0,1,0,1,0,1,2,3,2,3,2,3,4,5,4,5,4,5,6,7,
%U A276090 6,7,6,7,0,1,0,1,0,1,2,3,2,3,2,3,4,5,4,5,4,5,6,7,6,7,6,7,0,1,0,1,0,1,2,3,2,3,2,3,4,5,4,5,4,5,6,7,6,7,6,7,6
%N A276090 Left inverse of A276089: For n = sum_{i=1..} d(i)*i! (with each d(i) <= i), a(n) = sum_{j=1..} d(2j-1)*j!.
%C A276090 This "deaerates" A276089(n) by picking only the digits from the odd positions of its factorial base representation. Of course, when computed for an arbitrary n, those digits, when "compressed" into a(n) are not necessarily valid digits in standard factorial base representation (A007623).
%H A276090 Antti Karttunen, <a href="/A276090/b276090.txt">Table of n, a(n) for n = 0..20533</a>
%H A276090 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F A276090 Other identities. For all n >= 0:
%F A276090 a(A276089(n)) = n.
%e A276090 For n = 311 ("22321" in factorial base representation) we pick the digits at odd positions 1, 3 and 5, thus we get a(311) = 2*3! + 3*2! + 1*1! = 19.
%e A276090 For n=373 ("30201"), we pick the digits from those same positions and construct a(373) = 3*3! + 2*2! + 1*1! = 23.
%o A276090 (MIT/GNU Scheme)
%o A276090 ;; Standalone program:
%o A276090 (define (A276090 n) (let loop ((n n) (s 0) (f 1) (i 2) (j 2)) (if (zero? n) s (let ((d (modulo n j))) (loop (floor->exact (/ (/ (- n d) j) (+ 1 j))) (+ s (* f d)) (* i f) (+ 1 i) (+ 2 j))))))
%Y A276090 Left inverse of A276089.
%Y A276090 For no apparent reason, the terms a(0)..a(21) are equal to the terms a(3)..a(24) of A118777.
%Y A276090 Cf. A007623.
%K A276090 nonn,base
%O A276090 0,7
%A A276090 _Antti Karttunen_, Aug 19 2016