

A095372


1+integers repeating "90" decimal digit pattern:.


15



1, 91, 9091, 909091, 90909091, 9090909091, 909090909091, 90909090909091, 9090909090909091, 909090909090909091, 90909090909090909091, 9090909090909090909091, 909090909090909090909091
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OFFSET

0,2


COMMENTS

These numbers arise for example as divisors of several repunits (A002275).
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 3parameter family of 4thorder linear divisibility sequences found by Williams and Guy.  Peter Bala, Aug 22 2019
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


LINKS



FORMULA

a(n) = 101*a(n1)100*a(n2). G.f.: (10*x1) / ((x1)*(100*x1)).  Colin Barker, Jul 03 2013


EXAMPLE

Digitpattern P=[ab..z] repeating integers equal formally with P*(1+10^(Ln))/(1+10^L), where L is the length of pattern;


MATHEMATICA

Table[1+90*(100^n1)/99, {n, 0, 20}]


CROSSREFS



KEYWORD

nonn,easy,base


AUTHOR



STATUS

approved



