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.

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, 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, 19, 0, 5, 8, 0, 4, 8, 4, 3, 32, 0, 7, 32, 4, 7, 4, 3, 9, 34, 0, 10, 57

Offset: 1

Author

William Phoenix Marcum, Oct 05 2020

Keywords

• nonn

Comments

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.

Examples

			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.
		

Links

• William Phoenix Marcum, Table of n, a(n) for n = 1..10000
• William Marcum, Desmos graph

Crossrefs

Cf. A181391.

Programs

JavaScript

function a(n) {
  var seq = [1];
  var accseq = [];
  for (var i = 1; i < n; i++) {
    if (accseq.indexOf(seq[seq.length-1]) == -1) {
      seq.push(0);
    } else {
      seq.push(seq.length-accseq.indexOf(seq[seq.length-1]));
      accseq[accseq.indexOf(seq[seq.length-2])] = null;
    }
    accseq.push(seq[seq.length-2]);
  }
  return seq[seq.length-1];
}

Formula

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