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 A352111 #10 Mar 08 2022 11:36:43
%S A352111 0,1,-2,-1,-4,-3,6,7,4,5,2,3,12,13,10,11,8,9,18,19,16,17,14,15,-24,
%T A352111 -23,-26,-25,-28,-27,-18,-17,-20,-19,-22,-21,-12,-11,-14,-13,-16,-15,
%U A352111 -6,-5,-8,-7,-10,-9,-48,-47,-50,-49,-52,-51,-42,-41,-44,-43,-46,-45
%N A352111 In the factorial base expansion of n, replace each place value, say k! with k > 0, by (-1)^(k-1) * k!.
%C A352111 This sequence maps natural numbers uniquely onto integers.
%H A352111 Rémy Sigrist, <a href="/A352111/b352111.txt">Table of n, a(n) for n = 0..5039</a> (terms for n < 7!)
%H A352111 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%e A352111 For n = 42:
%e A352111 - 42 = 1 * 4! + 3 * 3! + 0 * 2! + 0 * 1!,
%e A352111 - so a(42) = 1 * -4! + 3 * 3! + 0 * -2! + 0 * 1! = -6.
%o A352111 (PARI) a(n) = { my (f=1, v=0); for (r=2, oo, if (n, v+=f*(n%r); n\=r; f*=-r, return (v))) }
%Y A352111 See A053985, A065369, A073835, A352112 for similar sequences.
%Y A352111 Cf. A000142, A108731.
%K A352111 sign,base
%O A352111 0,3
%A A352111 _Rémy Sigrist_, Mar 05 2022