The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A075002 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A075002

a(n) = smallest k such that A007908(k) is divisible by n.
(history; published version)

#11 by Charles R Greathouse IV at Sun Oct 11 23:45:58 EDT 2015

STATUS

editing

approved

#10 by Charles R Greathouse IV at Sun Oct 11 23:45:55 EDT 2015

PROG

(PARI) a(n)=my(m=Mod(1, n), k=1); while(m, m=10^#Str(k++)*m+k); k \\ Charles R Greathouse IV, Oct 11 2015

CROSSREFS

Cf. A007908.

STATUS

proposed

editing

#9 by Rick L. Shepherd at Sun Oct 11 21:42:34 EDT 2015

STATUS

editing

proposed

#8 by Rick L. Shepherd at Sun Oct 11 21:39:48 EDT 2015

COMMENTS

The maximum of the first 10000 terms is a(6314) = 1002902 and A007908(1002902) is a 5902910-digit number. - Rick L. Shepherd, Oct 11 2015

LINKS

Rick L. Shepherd, <a href="/A075002/b075002.txt">Table of n, a(n) for n = 1..10000</a>

STATUS

approved

editing

#7 by Max Alekseyev at Wed Sep 30 00:10:47 EDT 2015

STATUS

editing

approved

#6 by Max Alekseyev at Wed Sep 30 00:10:20 EDT 2015

EXAMPLE

a(4) = 2 as since A007908(2)=12 is divisible by 4.

a(7) = 11 as 7 divides A007908(11)=1234567891011 and 7 does not divide any smaller concatenations.

STATUS

approved

editing

#5 by Max Alekseyev at Wed Sep 30 00:09:15 EDT 2015

STATUS

editing

approved

#4 by Max Alekseyev at Wed Sep 30 00:09:09 EDT 2015

NAME

Smallest a(n) = smallest k such that concatenation 1 to A007908(k ) is divisible by n; or 0 if no such number exists.

COMMENTS

Conjecture: For every n there exists a nonzero k such that , a(n) = kis well-defined.

EXAMPLE

a(4)= 2 as 12 is divisible by 4. a(7) = 11 as 7 divides 1234567891011 and 7 does not divide any smaller concatenations.

a(7) = 11 as 7 divides 1234567891011 and 7 does not divide any smaller concatenations.

CROSSREFS

Cf. A007908

EXTENSIONS

Edited by Max Alekseyev, Sep 30 2015

STATUS

approved

editing

#3 by N. J. A. Sloane at Thu Dec 05 19:55:34 EST 2013

AUTHOR

_Amarnath Murthy (amarnath_murthy(AT)yahoo.com), _, Sep 01 2002

Discussion

Thu Dec 05

19:55

OEIS Server: https://oeis.org/edit/global/2075

#2 by N. J. A. Sloane at Sat Jun 12 03:00:00 EDT 2004

COMMENTS

Conjecture: For every n there exists a non-zero nonzero k such that a(n) = k.

KEYWORD

base,nonn,new