A152597 Where records occur in A001917.

2, 4, 11, 21, 31, 110, 124, 185, 279, 399, 716, 1028, 4552, 6207, 6543, 11424, 11557, 12251, 16199, 23043, 43390, 155798, 203095, 457523, 699782, 865318, 1294026, 2918851, 5635889, 6459777, 8999147, 9213126, 22383796, 28194383, 32131750, 105097565, 404165580

Offset: 1

Author

Klaus Brockhaus, Dec 09 2008

Keywords

• nonn

Examples

			First few terms of A001917 (has offset 2) are 1, 1, 2, 1, 1, 2, 1, 2, 1, 6, so a(1) to a(3) are 2, 4, 11.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..47

Crossrefs

Cf. A001917 ((p-1)/x, where p = prime(n) and x = smallest positive integer such that 2^x == 1 mod p), A152598 (records in A001917), A000720, A226216.

Programs

Magma

W:=[]; r:=0; for n in [2..100000] do p:=NthPrime(n); a:=(p-1)/Modorder(2, p); if r lt a then r:=a; Append(~W,n); end if; end for; print W;

Python

from itertools import islice
from sympy import nextprime, n_order
def agen():
    record, v, p = -1, 1, 3
    while True:
        if v > record: record = v; yield record
        v, p = (p-1)//n_order(2, p), nextprime(p)
print(list(islice(agen(), 20))) # Michael S. Branicky, Oct 09 2022

Formula

a(n) = A000720(A226216(n)). - Amiram Eldar, Nov 16 2023

Extensions

a(27)-a(37) from Amiram Eldar, Mar 08 2019