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 A095372 1+integers repeating "90" decimal digit pattern:. 9
 1, 91, 9091, 909091, 90909091, 9090909091, 909090909091, 90909090909091, 9090909090909091, 909090909090909091, 90909090909090909091, 9090909090909090909091, 909090909090909090909091 (list; graph; refs; listen; history; text; internal format)
 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 3-parameter family of 4th-order 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 H. C. Williams and R. K. Guy, Some fourth-order linear divisibility sequences, Intl. J. Number Theory 7 (5) (2011) 1255-1277. H. C. Williams and R. K. Guy, Some Monoapparitic Fourth Order Linear Divisibility Sequences Integers, Volume 12A (2012) The John Selfridge Memorial Volume. Index entries for linear recurrences with constant coefficients, signature (101,-100). FORMULA a(n) = 1+90*(-1+100^n)/99 = (10^(2n+1)+1)/11. - Rick L. Shepherd, Aug 01 2004 a(n) = (a(n-1)-1)*100+91, with a(0)=1. - Paolo P. Lava, Oct 21 2008 a(n) = 101*a(n-1)-100*a(n-2). G.f.: -(10*x-1) / ((x-1)*(100*x-1)). - Colin Barker, Jul 03 2013 EXAMPLE Digit-pattern P=[ab..z] repeating integers equal formally with P*(-1+10^(Ln))/(-1+10^L), where L is the length of pattern; a(9) divides A002275(38) repunit. See A095371. MATHEMATICA Table[1+90*(100^n-1)/99, {n, 0, 20}] CROSSREFS Cf. A002275, A095371. Cf. A015585, A097209, A001562, A054416, A152577, A100047. Cf. A329914, A329915. Sequence in context: A006244 A054216 A109627 * A165154 A015261 A168624 Adjacent sequences:  A095369 A095370 A095371 * A095373 A095374 A095375 KEYWORD nonn,easy,base AUTHOR Labos Elemer, Jun 07 2004 STATUS approved

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Last modified July 13 10:13 EDT 2020. Contains 335687 sequences. (Running on oeis4.)