A360805 Nonnegative integers k such that k! mod nextprime(k) is larger than k.

0, 31, 120, 283, 293, 712, 2872, 3287, 5028, 5129, 7088, 9553, 13229, 14232, 14799, 15113, 20153, 20830, 23239, 30233, 31430, 31667, 34443, 40654, 44298, 50184, 78877, 105834, 115281, 125120, 164253, 192103, 201590, 227747, 239910, 241910, 282230, 322550, 374370

Offset: 1

Author

Alois P. Heinz, Feb 22 2023

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..213

Crossrefs

Cf. A000142, A007978, A151800, A360825.

Programs

Maple

q:= n-> is(n! mod nextprime(n)>n):
select(q, [$0..20000])[];

Python

from itertools import count, islice
from functools import reduce
from sympy import nextprime
def A360805_gen(startvalue=0): # generator of terms >= startvalue
    n = max(startvalue,0)
    m = nextprime(n)
    while True:
        a = m-1
        klist = []
        for i in range(m-1,n,-1):
            a = a*pow(i,-1,m)%m
            if a>i-1:
                klist.append(i-1)
        yield from sorted(klist)
        n, m = m, nextprime(m)
A360805_list = list(islice(A360805_gen(),30)) # Chai Wah Wu, Feb 24 2023

Formula

{ k >= 0 : k! mod nextprime(k) > k }.

A360825(a(n)) > a(n).