cp's OEIS Frontend

A337980 When terms first appear in the sequence they are "untouched". Start with a(1)=1. Thereafter, to find a(n), let k = a(n-1). If there is an earlier occurrence a(n-m) = k which is untouched, then a(n) = m and a(n-m) is now "touched". Otherwise, a(n) = 0.

%I A337980 #44 Dec 22 2024 09:08:39
%S A337980 1,0,0,2,0,3,0,3,3,2,7,0,6,0,3,7,6,5,0,6,4,0,4,3,10,0,5,10,4,7,15,0,7,
%T A337980 4,6,16,0,6,4,6,3,18,0,7,12,0,4,9,0,4,4,2,43,0,6,16,21,0,5,33,0,4,12,
%U A337980 19,0,5,8,0,4,8,4,3,32,0,7,32,4,7,4,3,9,34,0,10,57
%N A337980 When terms first appear in the sequence they are "untouched". Start with a(1)=1. Thereafter, to find a(n), let k = a(n-1). If there is an earlier occurrence a(n-m) = k which is untouched, then a(n) = m and a(n-m) is now "touched". Otherwise, a(n) = 0.
%C A337980 Similar to the Van Eck sequence A181391, except (1) A181391 starts with a 0 instead of a 1, and (2) in A181391 each nonzero term a(n) = m-1 instead of m as in the definition above.
%H A337980 William Phoenix Marcum, <a href="/A337980/b337980.txt">Table of n, a(n) for n = 1..10000</a>
%H A337980 William Marcum, <a href="https://www.desmos.com/calculator/gzvgcb9zgk">Desmos graph</a>
%F A337980 b(n)=0 => a(n+1)=0; b(n)>0 => a(n+1)=b(n)+1; where b=A181391. - _Jan Ritsema van Eck_, Jan 09 2021
%e A337980 a(1) = 1. There is no untouched 1 before a(1), so a(2) = 0. There is no untouched 0 before a(2), so a(3) = 0. a(2) = 0, so a(4) = 2 and a(2) is marked "touched" (we can't use it again, but it is still in the sequence). No untouched 2 yet, so a(5) = 0. a(2) = 0, but it has been touched, while a(3) = 0, so a(6) = 2.
%o A337980 (JavaScript) function a(n) {
%o A337980   var seq = [1];
%o A337980   var accseq = [];
%o A337980   for (var i = 1; i < n; i++) {
%o A337980     if (accseq.indexOf(seq[seq.length-1]) == -1) {
%o A337980       seq.push(0);
%o A337980     } else {
%o A337980       seq.push(seq.length-accseq.indexOf(seq[seq.length-1]));
%o A337980       accseq[accseq.indexOf(seq[seq.length-2])] = null;
%o A337980     }
%o A337980     accseq.push(seq[seq.length-2]);
%o A337980   }
%o A337980   return seq[seq.length-1];
%o A337980 }
%Y A337980 Cf. A181391.
%K A337980 nonn
%O A337980 1,4
%A A337980 _William Phoenix Marcum_, Oct 05 2020