

A301427


Least nonnegative integer k such that n!  n  k is prime.


1



0, 1, 2, 5, 10, 23, 4, 1, 2, 1, 10, 3, 32, 37, 42, 23, 82, 11, 10, 51, 66, 49, 124, 11, 16, 73, 2, 49, 30, 131, 14, 159, 78, 91, 60, 41, 34, 43, 90, 37, 66, 65, 8, 43, 32, 55, 10, 47, 128, 15, 6, 73, 6, 405, 220, 51, 78, 79, 10, 9, 38, 295, 62, 251, 124, 183, 34, 27, 680, 91, 300
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

3,3


COMMENTS

The (n1) consecutive numbers n!n, ... , n!2 (for n > 3) are not prime.


LINKS

Seiichi Manyama, Table of n, a(n) for n = 3..500


FORMULA

a(n) = A037155(n)  n.


EXAMPLE

a(3)=0 because 3!  3  0 = 3 is prime.
a(4)=1 because 4!  4  1 = 19 is prime and 20 is not.
a(5)=2 because 5!  5  2 = 113 is prime and 114 and 115 are not prime.


MAPLE

f:= proc(n) local r; r:= n!n;
r  prevprime(r)
end proc:
f(3):= 0:
seq(f(i), i=3..100); # Robert Israel, Mar 23 2018


MATHEMATICA

a[n_] := n!  NextPrime[n!  1, 1]  n;
a /@ Range[3, 100] (* JeanFrançois Alcover, Oct 26 2020 *)


PROG

(PARI) a(n) = apply(x>(xprecprime(x)), n!n);
vector(99, n, a(n+2)) \\ Altug Alkan, Mar 21 2018


CROSSREFS

Cf. A037155, A073443, A090786.
Sequence in context: A046745 A198950 A015902 * A300275 A226455 A284139
Adjacent sequences: A301424 A301425 A301426 * A301428 A301429 A301430


KEYWORD

nonn


AUTHOR

Seiichi Manyama, Mar 21 2018


STATUS

approved



