

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
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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 28899digit probable prime 851777...777, which eliminated 851 as a possible prefix for the 7case. 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 7case 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), 153160.
Lenny Jones and Maria Markovich, Generating Composite Sequences by Appending Digits to Special Types of Integers, Fibonacci Quart. 52 (2014), no. 2, 148159.
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(n1) + 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



