A257277 a(n+1) has a digit that divides a(n) and is the least positive integer not appearing earlier with this property.

0, 1, 10, 2, 11, 12, 3, 13, 14, 7, 15, 5, 16, 4, 17, 18, 6, 19, 21, 23, 31, 41, 51, 30, 20, 22, 24, 8, 25, 35, 27, 9, 29, 61, 71, 81, 32, 26, 28, 34, 42, 33, 36, 37, 91, 47, 100, 40, 38, 52, 43, 101, 102, 39, 53, 103, 104, 44, 45, 49, 57, 63, 59, 105, 50, 54, 46, 62, 72, 48, 56, 58, 82, 92, 64, 68, 74, 106, 107, 108, 60, 55, 65, 75, 73, 109, 110, 85

Offset

0,3

Comments

A variant of A248024.

This is a permutation of the nonnegative integers, see A257276 for the inverse permutation.

There are large ranges of fixed points, e.g., between a(135) = 99 and a(200) = 201, or between a(1080) = 999 and a(2000) = 2001. For indices n in these ranges, the sequence restricted to [0...n] is a permutation (i.e., all numbers up to n appear among the values up to that point).

If one requires that a(n+1) has *no* digit dividing a(n), the sequence starts 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 20, 30, 40, 33, 22, 34, ... and stops at a(1422) = 2520, divisible by any digit. If one requires the sequence to be increasing, then it goes ..., 20, 30, 40, 60, 70, 80, 90, 400, 600, 700, 800, 900, 7000, 9000, 70000, 90000, 700000, 900000, ...

Links

M. F. Hasler, Table of n, a(n) for n = 0..1199

E. Angelini, Division by digits (variation), SeqFan list, May 7, 2015.

Prog

(PARI) {u=n=0; until(print1(n", "), u+=1<<n; d=select(i->!(n%i), vector(9, i, i)); n=0; until(!bittest(u, n++)&&setintersect(d, Set(digits(n))), ))}

Crossrefs

Cf. A248024, A257276.

Sequence in context: A365625 A323821 A351840 * A248024 A269631 A334737

Adjacent sequences: A257274 A257275 A257276 * A257278 A257279 A257280

Keyword

nonn,base,look

Author

Eric Angelini and M. F. Hasler, May 07 2015

Status

approved