OFFSET

1,2

COMMENTS

The integers m counted are A038772 so that A038772(a(n)) is the last there of n digits and A038772(a(n)+1) is the first there of n+1 digits, for n>=2.

The digit divisibility condition is a regular language so a(n) is a linear recurrence. Working through a state machine for A038772 (or its complement A038770) shows the recurrence is order 983, though its characteristic polynomial factorizes over rationals into terms of orders at most 36. The recurrence begins at a(4..986) giving a(987). See the links for recurrence coefficients and generating function.

The biggest root (by magnitude) of the characteristic polynomial is 9 and its g.f. coefficient is 4/21 which shows a(n) -> (4/21)*9^n.

LINKS

FORMULA

a(n) = 10^n-1 - A327560(n).

CROSSREFS

KEYWORD

nonn,base

AUTHOR

Kevin Ryde, Sep 19 2019

STATUS

approved