

A230459


Ordered by increasing m with k<m, a(n) is the nth record value of gcd(k!+1,m!+1).


1



2, 7, 71, 661, 733, 2371, 3529, 13499, 46549, 98101, 163517, 197933, 1924217, 3322441, 5370731
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OFFSET

1,1


COMMENTS

The pairs (m,k) generating records are (1,0), (6,3), (9,7), (17,8), (89,51), (174,144), (349,228), (422,81), (650,406), (1415,1718), (1697,161), (1622,773), (1884,1219), (7003,2031) and (17057,660).
Heuristics in concert with a database of 'small' (less than, say, 10^12) prime factors of numbers of this kind would generate faster accurate results with near certainty, while any truly proving program is doomed to be relatively slow by comparison (and see following on a(15)).
Note: An auxiliary program employed a limit of 10^8in lieu of a databaseto generate the likelybutnotcertain value of a(15) shown last.


LINKS

Table of n, a(n) for n=1..15.


EXAMPLE

a(1)=2, corresponding to m=1 and k=0. 7 is the first value other than 1 to be the greatest common divisor of two different numbers k!+1 and m!+1, where m is increasing and k is allowed to increase to m1 for a given m (For m=6 and k=3, m!+1=7*103 and k!+1=7); so that a(2)=7.


PROG

(PARI)
{
\\ The constant L here is arbitrary.\\
\\ This does not generate a(1).\\
rec=2; L=10000; F=vector(L); n=2;
for(k=1, L, n; n*=k; n++; F[k]=n);
for(m=2, L,
for(k=1, m1,
a=gcd(F[m], F[k]); if(a>rec,
rec=a; print1(a": "m", "k"\n"))))
}


CROSSREFS

A038507, A051301, A002583, A002981
Sequence in context: A106917 A188665 A198188 * A267406 A100360 A061421
Adjacent sequences: A230456 A230457 A230458 * A230460 A230461 A230462


KEYWORD

nonn,more


AUTHOR

James G. Merickel, Oct 19 2013


STATUS

approved



