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 A276089 #12 Aug 21 2016 17:45:02
%S A276089 0,1,6,7,12,13,120,121,126,127,132,133,240,241,246,247,252,253,360,
%T A276089 361,366,367,372,373,5040,5041,5046,5047,5052,5053,5160,5161,5166,
%U A276089 5167,5172,5173,5280,5281,5286,5287,5292,5293,5400,5401,5406,5407,5412,5413,10080,10081,10086,10087,10092,10093,10200,10201,10206,10207,10212,10213,10320,10321
%N A276089 Factorial base representation of n is aerated (and then converted back to decimal): for n = sum_{i=1..} digit(i)*i! (with each digit(i) <= i), a(n) = sum_{i=1..} digit(i)*(2i-1)!.
%C A276089 Here "aeration" means inserting zeros between the digits of factorial base representation of n. See the examples.
%H A276089 Antti Karttunen, <a href="/A276089/b276089.txt">Table of n, a(n) for n = 0..5039</a>
%H A276089 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F A276089 When n = sum_{i=1..A084558(n)} d(i)*i! (which is unique representation as long as each d(i) <= i) then a(n) = sum_{i=1..A084558(n)} d(i)*(2i-1)!, where A084558(n) gives the length of factorial base representation of n.
%F A276089 Other identities. For all n >= 0:
%F A276089 A276090(a(n)) = n.
%e A276089 n A007623(n) "aerated" and converted back to decimal gives
%e A276089 a(n)
%e A276089 0 0 0 0
%e A276089 1 1 1 1
%e A276089 2 10 100 6
%e A276089 3 11 101 7
%e A276089 4 20 200 12
%e A276089 5 21 201 13
%e A276089 6 100 10000 120
%e A276089 7 101 10001 121
%e A276089 8 110 10100 126
%e A276089 9 111 10101 127
%e A276089 10 120 10200 132
%e A276089 11 121 10201 133
%e A276089 12 200 20000 240
%e A276089 13 201 20001 241
%e A276089 14 210 20100 246
%e A276089 15 211 20101 247
%e A276089 16 220 20200 252
%e A276089 17 221 20201 253
%e A276089 18 300 30000 360
%e A276089 19 301 30001 361
%e A276089 20 310 30100 366
%e A276089 21 311 30101 367
%e A276089 22 320 30200 372
%e A276089 23 321 30201 373
%o A276089 (Scheme)
%o A276089 ;; Standalone program:
%o A276089 (define (A276089 n) (let loop ((n n) (s 0) (f 1) (i 2) (j 2)) (if (zero? n) s (let ((d (modulo n i))) (loop (/ (- n d) i) (+ s (* f d)) (* j (+ 1 j) f) (+ 1 i) (+ 2 j))))))
%Y A276089 Cf. A000142, A007623, A084558
%Y A276089 Cf. A276090 (a left inverse).
%Y A276089 Cf. A275959 (subsequence).
%K A276089 nonn,base
%O A276089 0,3
%A A276089 _Antti Karttunen_, Aug 19 2016