A119354 - OEIS

A119354

Smallest number which does not use digit n-1 written in base n, but does use digit b-1 written in base b for any 1<b<n.

0, 1, 2, 7, 14, 23, 139, 47, 485, 319, 989, 239, 5927, 23319, 27719, 13679, 57119, 159119, 746927, 500399, 1627919, 2585519, 3694397, 7305479, 17067599, 82265039, 384812999, 41126399, 61483967, 586370399, 589188599, 2196179999, 1770310079, 51515219183, 12415603199, 1278033119, 24126046559

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,3

COMMENTS

From Michael S. Branicky, Sep 08 2025: (Start)

a(36) = 12415603199, a(37) = 1278033119.

a(35) and a(38..oo) > 2*10^9. (End)

From David A. Corneth, Sep 10 2025: (Start)

We can ease the search a little bit.

In a search for a(n) if we test some number t and the number t does not have a digit b-1 for some 1 < b < n then we can reset t to the smallest number > t that has a digit b-1. That is set t to t + b-1 - t%b.

For example in a search for a(8) we might be testing 48 and see that 48 = 120_6 which does not contain a digit 6-1. The next number larger than 48 that does contain a digit 5 in base 6 is 48 + 5 - (48%6).

Also if we test a number t in a search for a(n) and see that it has a digit n-1 in base n then we can reset it to the smallest number > t that has no digit n-1 in base n.

For example in our search for a(8) we might be checking 57 = 71_8 which has a digit n-1 in base n. We can reset it to "80_8" = 100_8 = 64 by increasing the 7 by 1 and setting all less significant digits to 0.

In the search for a(35) and a(38) it was sufficient to check just about 1 in 19 numbers this way. (End)

LINKS

Table of n, a(n) for n=2..38.

FORMULA

A119352(a(n)) = n and A119352(m) != n for m < a(n). - Reinhard Zumkeller, Apr 12 2015

PROG

(Haskell)

import Data.List (elemIndex); import Data.Maybe (fromJust)

a119354 = fromJust . (`elemIndex` a119352_list)

-- Reinhard Zumkeller, Apr 12 2015

CROSSREFS

Cf. A106372, A119352.