|
|
A090086
|
|
Smallest pseudoprime to base n, not necessarily exceeding n (cf. A007535).
|
|
18
|
|
|
4, 341, 91, 15, 4, 35, 6, 9, 4, 9, 10, 65, 4, 15, 14, 15, 4, 25, 6, 21, 4, 21, 22, 25, 4, 9, 26, 9, 4, 49, 6, 25, 4, 15, 9, 35, 4, 39, 38, 39, 4, 205, 6, 9, 4, 9, 46, 49, 4, 21, 10, 51, 4, 55, 6, 15, 4, 57, 15, 341, 4, 9, 62, 9, 4, 65, 6, 25, 4, 69, 9, 85, 4, 15, 74, 15, 4, 77, 6, 9, 4, 9, 21, 85, 4, 15, 86, 87, 4, 91, 6
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Conjecture: a(n) = A007535(n) for finitely many n. For n > 2; if a(n) > n, then n-1 is prime (find all these primes). - Thomas Ordowski, Aug 09 2018
It seems that if a(2^p) = p^2, then 2^p-1 is prime. - Thomas Ordowski, Aug 10 2018
|
|
LINKS
|
|
|
FORMULA
|
a(n) = LeastComposite{x; n^(x-1) mod x = 1}.
|
|
EXAMPLE
|
a(n) = 4 for n = 1 + 4*k, k >= 0.
a(n) = 6 for n = 7 + 12*k, k >= 0.
a(n) = 9 for n = 8 + 18*k, 10 + 18*k, 35 + 36*k, k >= 0.
(End)
a(n) = 10 for n = 51 + 60*k, 11 + 180*k, 131 + 180*k, k >= 0.
|
|
MATHEMATICA
|
f[n_] := Block[{k = 1}, While[ GCD[n, k] > 1 || PrimeQ[k] || PowerMod[n, k - 1, k] != 1, j = k++]; k]; Array[f, 91] (* Robert G. Wilson v, Feb 26 2015 *)
|
|
PROG
|
(PARI) /* a(n) <= 2000 is sufficient up to n = 10000 */
a(n) = for(k=2, 2000, if((n^(k-1))%k==1 && !isprime(k), return(k))) \\ Eric Chen, Feb 22 2015
(PARI) a(n) = {forcomposite(k=2, , if (Mod(n, k)^(k-1) == 1, return (k)); ); } \\ Michel Marcus, Mar 02 2015
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|