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 A095372 #42 Mar 16 2025 12:20:47
%S A095372 1,91,9091,909091,90909091,9090909091,909090909091,90909090909091,
%T A095372 9090909090909091,909090909090909091,90909090909090909091,
%U A095372 9090909090909090909091,909090909090909090909091
%N A095372 1+integers repeating "90" decimal digit pattern.
%C A095372 These numbers arise for example as divisors of several repunits (A002275).
%C A095372 The aerated sequence A(n) = [1, 0, 91, 0, 9091, 0, 909091,...] is a divisibility sequence, i.e., A(n) divides A(m) whenever n divides m. It is the case P1 = 0, P2 = -11^2, Q = 10 of the 3-parameter family of 4th-order linear divisibility sequences found by Williams and Guy. - _Peter Bala_, Aug 22 2019
%C A095372 Except for a(0) = 1, these terms M are such that 21 * M = 1M1, where 1M1 denotes the concatenation of 1, M and 1. Actually 21 is A329914(1) and a(1) = A329915(1) = 91, and the terms >=91 form the set {M_21}; for example, 21 * 909091 = 1(909091)1. - _Bernard Schott_, Dec 01 2019
%H A095372 H. C. Williams and R. K. Guy, <a href="http://dx.doi.org/10.1142/S1793042111004587">Some fourth-order linear divisibility sequences</a>, Intl. J. Number Theory 7 (5) (2011) 1255-1277.
%H A095372 H. C. Williams and R. K. Guy, <a href="https://www.emis.de/journals/INTEGERS/papers/a17self/a17self.Abstract.html">Some Monoapparitic Fourth Order Linear Divisibility Sequences</a> Integers, Volume 12A (2012) The John Selfridge Memorial Volume.
%H A095372 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (101,-100).
%F A095372 a(n) = 1 + 90*(-1 + 100^n)/99 = (10^(2*n+1) + 1)/11. - _Rick L. Shepherd_, Aug 01 2004
%F A095372 From _Colin Barker_, Jul 03 2013: (Start)
%F A095372 a(n) = 101*a(n-1) - 100*a(n-2).
%F A095372 G.f.: -(10*x-1)/((x-1)*(100*x-1)). (End)
%F A095372 E.g.f.: exp(x)*(1 + 10*(exp(99*x) - 1)/11). - _Elmo R. Oliveira_, Mar 15 2025
%e A095372 Digit-pattern P=[ab..z] repeating integers equal formally with P*(-1+10^(Ln))/(-1+10^L), where L is the length of pattern;
%e A095372 a(9) divides A002275(38) repunit. See A095371.
%t A095372 Table[1+90*(100^n-1)/99, {n, 0, 20}]
%Y A095372 Cf. A002275, A095371.
%Y A095372 Cf. A001562, A015585, A054416, A097209, A100047, A152577.
%Y A095372 Cf. A329914, A329915.
%K A095372 nonn,easy,base
%O A095372 0,2
%A A095372 _Labos Elemer_, Jun 07 2004