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A187078 38 followed by n ones. 1
38, 381, 3811, 38111, 381111, 3811111, 38111111, 381111111, 3811111111, 38111111111, 381111111111, 3811111111111, 38111111111111, 381111111111111, 3811111111111111, 38111111111111111, 381111111111111111, 3811111111111111111, 38111111111111111111, 381111111111111111111 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Jones proves that 38 is the smallest composite number that produces only composite numbers when 1 is repeatedly appended to it.

Stan Wagon, who is working on similar numbers ending in 3, 7, and 9, reports that the upper bounds for those numbers are 4070, 891, and 10175, respectively. - T. D. Noe, Mar 08 2011

Today Stan Wagon found a 28899-digit probable prime 851777...777, which eliminated 851 as a possible prefix for the 7-case. Because it is easy to show the 891777...777 is composite for any number of 7's, this means that 891 is the solution for the 7-case of this problem. - T. D. Noe, Mar 08 2011

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Lenny Jones, When does appending the same digit repeatedly on the right of a positive integer generate a sequence of composite integers?, Amer. Math. Monthly, 118 (2011), 153-160.

Lenny Jones and Maria Markovich, Generating Composite Sequences by Appending Digits to Special Types of Integers, Fibonacci Quart. 52 (2014), no. 2, 148-159.

Michael Penn, From the Benelux Math Olympiad., YouTube video, 2021.

Index entries for linear recurrences with constant coefficients, signature (11,-10).

FORMULA

From Bruno Berselli, Mar 09 2011: (Start)

G.f.: (38 - 37*x)/((1 - x)*(1 - 10*x)).

a(n) = (343*10^n - 1)/9. (End)

a(n) = 10*a(n-1) + 1 with n>0, a(0)=38. - Vincenzo Librandi, Jun 07 2011

MATHEMATICA

t = {38}; Do[AppendTo[t, 10*t[[-1]] + 1], {19}]; t

NestList[10#+1&, 38, 20] (* Harvey P. Dale, Sep 20 2017 *)

PROG

(MAGMA) [Seqint([1: n in [1..k]] cat Intseq(38)): k in [0..19]]; // Bruno Berselli, Mar 09 2011

(PARI) a(n)=343*10^n\9 \\ Charles R Greathouse IV, Sep 24 2012

CROSSREFS

Sequence in context: A156661 A249711 A220918 * A155193 A159943 A221634

Adjacent sequences:  A187075 A187076 A187077 * A187079 A187080 A187081

KEYWORD

nonn,base,easy

AUTHOR

T. D. Noe, Mar 03 2011

STATUS

approved

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Last modified July 29 09:41 EDT 2021. Contains 346344 sequences. (Running on oeis4.)