This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A327561 #17 Aug 22 2021 13:29:49 %S A327561 0,31,291,2421,20047,167493,1414416,12055582,103547007,895037251, %T A327561 7777564986,67886919436,594812780492,5228677322789,46092207649088, %U A327561 407310913585540,3607044214789103,32002805595571724,284404590208016926 %N A327561 The number of integers m in the range 0 < m < 10^n which are not divisible by any of their own digits (A038772). %C A327561 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. %C A327561 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. %C A327561 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. %H A327561 Kevin Ryde, <a href="/A327561/b327561.txt">Table of n, a(n) for n = 1..1047</a> %H A327561 Kevin Ryde, <a href="/A327561/a327561.gp.txt">Linear recurrence coefficients and generating function, in a PARI/GP script</a> %H A327561 <a href="/index/Rec#order_983">Index entries for linear recurrences with constant coefficients</a>, order 983. %F A327561 a(n) = 10^n-1 - A327560(n). %Y A327561 Cf. A038770, A038772, A327560. %K A327561 nonn,base %O A327561 1,2 %A A327561 _Kevin Ryde_, Sep 19 2019