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A259230 a(n) = smallest k such that (A115091(n)-k)! == -1 (mod A115091(n)^2). 1
1, 6, 1, 24, 64, 1, 384 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The values of m in A115091.

A115091(n) is in A007540 iff a(n) = 1.

LINKS

Table of n, a(n) for n=1..7.

EXAMPLE

a(2) = 6, because 6 is the smallest k such that (A115091(2)-k)! == -1 (mod A115091(2)^2), which yields the congruence (11-6)! == -1 (mod 11^2).

MATHEMATICA

t = Select[Prime@ Range@ 120, AnyTrue[Range@ #, Function[m, Divisible[m! + 1, #^2]]] &]; Table[k = 1; While[Mod[(t[[n]] - k)!, t[[n]]^2] != t[[n]]^2 - 1, k++]; k, {n, 7}] (* Michael De Vlieger, Nov 10 2015, Version 10 *)

PROG

(PARI) forprime(p=1, , for(k=1, p-1, if(Mod((p-k)!, p^2)==-1, print1(k, ", "); break({1}))))

CROSSREFS

Cf. A007540, A115091.

Sequence in context: A338865 A278958 A281631 * A278756 A147327 A145629

Adjacent sequences:  A259227 A259228 A259229 * A259231 A259232 A259233

KEYWORD

nonn,hard,more

AUTHOR

Felix Fröhlich, Nov 08 2015

STATUS

approved

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Last modified September 21 07:28 EDT 2021. Contains 347596 sequences. (Running on oeis4.)