login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A111027 Wieferich primes in base 12. 6
2693, 123653 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

I have searched up to the 9 millionth prime, 160481183 and gave up trying to find a third term. The sequence is conjectured to be infinite. If the behavior is similar to base 10, A045616, then the next term could be greater than 2*10^11. In base 12 with X for ten and E for eleven the sequence is [1685, 5E685] so it would be interesting to see if the third term ends in 685 as well. These primes are also the Wieferich numbers in base 12: 12^phi(n) = 1 mod n^2.

Richard Fischer has carried this search to 4.8 * 10^13 (as of January 2014). - John Blythe Dobson, Mar 06 2014

LINKS

Table of n, a(n) for n=1..2.

Richard Fischer, Fermatquotient B^(P-1) == 1 (mod P^2).

FORMULA

12^(p-1) == 1 mod p^2

MAPLE

WP:=[]: for z from 1 to 1 do for k from 1 to 9000000 do p:=ithprime(k); if 12 &^(p-1) mod p^2 = 1 then WP:=[op(WP), p]; printf("p=%d, ", p); fi; if k mod 10^5 = 0 then printf("k=%d, ", k); fi; od; od; WP;

CROSSREFS

Cf. A001220, A039951, A045616, A077815, A077816.

Sequence in context: A186937 A185748 A020424 * A245529 A210049 A115930

Adjacent sequences:  A111024 A111025 A111026 * A111028 A111029 A111030

KEYWORD

nonn,bref

AUTHOR

Walter Kehowski, Oct 05 2005

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 26 01:29 EST 2014. Contains 250017 sequences.