A080427 a(1)=1 and, for n>1, a(n) is the smallest positive integer such that the absolute difference |a(n)-a(n-1)| has not occurred previously.

1, 1, 2, 4, 1, 5, 10, 1, 7, 14, 1, 9, 19, 1, 12, 24, 1, 15, 30, 1, 17, 34, 1, 20, 40, 1, 22, 44, 1, 25, 50, 1, 27, 54, 1, 29, 59, 1, 32, 64, 1, 35, 70, 1, 37, 74, 1, 39, 79, 1, 42, 84, 1, 45, 90, 1, 47, 94, 1, 49, 99, 1, 52, 104, 1, 55, 110, 1, 57, 114, 1, 60, 120, 1, 62, 124, 1, 65, 130

Offset

1,3

Comments

It appears (1) that a(3n+2)=1 for n=1,2,3,... and (2) that the sequence {a(3n+3)-a(3n)}={3,2,2,3,3,2,3,2,3,2,2,3,3,2,2,3,3,2,...} consists only of 2's and 3's and that the sequence of the lengths of runs of consecutive 3's in {a(3n+3)-a(3n)} is given by {1,2,1,1,2,2,2,1,...}=A026465.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Formula

It appears that abs(a(n+2)-a(n+1)) = A101544(n) for any n > 0. - Rémy Sigrist, Apr 12 2020

Prog

(PARI) { my(s=0, v=1, d); for (n=1, 79, print1 (v, ", "); for (w=1, oo, if (!bittest(s, d=abs(v-w)), s+=2^d; v=w; break))) } \\ Rémy Sigrist, Apr 12 2020

Crossrefs

Cf. A026465, A067992, A101544.

Sequence in context: A308437 A201283 A283739 * A118906 A085059 A336164

Adjacent sequences: A080424 A080425 A080426 * A080428 A080429 A080430

Keyword

nonn

Author

John W. Layman, Feb 19 2003

Status

approved