A337707 a(n) is the lowest number in the sequence of the first occurrence of exactly n consecutive numbers with at least one repeated digit, or -1 if no such number exists.

11, 121, 99, 1898, 12898, 123898, 1234898, 12345898, 123456898, 110, 1909, 10330, 9188, 9088, 19787, 129787, 1239787, 12349787, 123459787, 1210, 12909, 103430, 1024540, 2988, 1988, 27987, 237987, 2347987, 23457987, 12310, 123909, 1034530, 10245640, 102356750, 988, 12988

Offset

1,1

Comments

Terms computed by Claudio Meller.

Does the term -1 first appear at a(55)?

All terms < 9876543210. - Robert Israel, Jan 14 2022

Links

Michel Marcus, Table of n, a(n) for n = 1..54

Michel Marcus, Positions and lengths

Michel Marcus, Lengths and positions

Example

a(3) = 99 is the smallest number in the first appearance sequence of 3 consecutive numbers with repeated digits, 99, 100 and 101, a(15) = 19787 is the smallest number in the first appearance sequence of 15 consecutive numbers with repeated digits that starts in 19787 and finish in 19801 (19802 has no repeated digits).

Prog

(PARI) isokd(n) = my(d=digits(n)); #d != #Set(d); \\ A109303
isok(k, n) = {if (! isokd(k-1), for (i=k, k+n-1, if (! isokd(i), return (0)); ); ! isokd(k+n); ); }
a(n) = {my(k=1); while (!isok(k, n), k++); k; } \\ Michel Marcus, Jan 13 2022
(PARI) lista(nn) = {my(map=Map(), r=isokd(1), nb, k, nbmax=0); for (n=2, nn, my(rr = isokd(n)); if (r, if (rr, nb++, if (! mapisdefined(map, nb), mapput(map, nb, k)); nb=0),  if (rr, nb=1; k=n, nb=0); ); r = rr; ); map; } \\ Michel Marcus, Jan 14 2022

Crossrefs

Cf. A109303.

Sequence in context: A004190 A089707 A223391 * A084969 A045592 A045595

Adjacent sequences: A337704 A337705 A337706 * A337708 A337709 A337710

Keyword

base,nonn

Author

Rodolfo Kurchan, Sep 26 2020

Status

approved