The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A181450

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A181450

Numbers n such that 11 is the largest prime factor of n^2 - 1.
(history; published version)

#13 by Charles R Greathouse IV at Thu Sep 08 08:45:54 EDT 2022

PROG

(MAGMAMagma) [ n: n in [2..20000] | m eq 11 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 18 2011

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#12 by Bruno Berselli at Mon May 07 03:49:07 EDT 2018

STATUS

reviewed

approved

#11 by Michel Marcus at Mon May 07 01:29:51 EDT 2018

STATUS

proposed

reviewed

#10 by Jon E. Schoenfield at Sun May 06 23:00:09 EDT 2018

STATUS

editing

proposed

#9 by Jon E. Schoenfield at Sun May 06 23:00:06 EDT 2018

NAME

Numbers n such that 11 is the largest prime factor of n^2 - 1.

PROG

(MAGMA) [ n: n in [2..20000] | m eq 11 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // _Klaus Brockhaus, _, Feb 18 2011

STATUS

approved

editing

#8 by Charles R Greathouse IV at Mon Jul 01 13:04:59 EDT 2013

STATUS

editing

approved

#7 by Charles R Greathouse IV at Mon Jul 01 13:03:53 EDT 2013

PROG

(PARI) is(n)=n=n^2-1; forprime(p=2, 7, n/=p^valuation(n, p)); n>1 && 11^valuation(n, 11)==n \\ Charles R Greathouse IV, Jul 01 2013

STATUS

approved

editing

#6 by Russ Cox at Sat Mar 31 10:22:17 EDT 2012

AUTHOR

_Artur Jasinski (grafix(AT)csl.pl), _, Oct 21 2010

Discussion

Sat Mar 31

10:22

OEIS Server: https://oeis.org/edit/global/339

#5 by T. D. Noe at Fri Feb 18 15:46:53 EST 2011

STATUS

proposed

approved

#4 by Klaus Brockhaus at Fri Feb 18 15:40:02 EST 2011

NAME

Numbers k n such that 11 is the largest prime factor of kn^2-1.

COMMENTS

This sequence Sequence is finite and complete, for proof see. A175607.

Search for terms can be restricted to the range from 2 to A175607(5) = 19601; primepi(11) = 5.

MATHEMATICA

jj=2^36*3^23*5^15*7^13*11^10*13^9*17^8*19^8*23^8*29^7*31^7*37^7*41^6*43^6*47^6*53^6*59^6*61^6*67^6*71^5*73^5*79^5*83^5*89^5*97^5;

rr ={}; n = 2; While[n < 100000, If[GCD[jj, n^2 - 1] == n^2 - 1, k = FactorInteger[n^2 - 1]; kk = Last[k][[1]]; If[kk == 11, AppendTo[rr, n]]]; n++ ]; rr (*Artur Jasinski*)

Select[Range[20000], FactorInteger[#^2-1][[-1, 1]]==11&]

PROG

(MAGMA) [ n: n in [2..20000] | m eq 11 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 18 2011

CROSSREFS

Cf. A175607, A175901-A175904, A181447-A181449, A181451-A181470, A181568.

KEYWORD

fini,full,nonn

STATUS

approved

proposed