A337980 - OEIS

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

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OFFSET

1,4

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.

LINKS

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

William Marcum, Desmos graph

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

EXAMPLE

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.

PROG

(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]);