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

1,2

Links

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

Formula

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

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

Maple

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

Prog

(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

Crossrefs

Cf. A000142, A007978, A151800, A360825.

Sequence in context: A010019 A256650 A131550 * A158558 A160893 A202994

Adjacent sequences: A360802 A360803 A360804 * A360806 A360807 A360808

Keyword

nonn

Author

Alois P. Heinz, Feb 22 2023

Status

approved