A152597 - OEIS

%I #15 Nov 16 2023 07:44:02

%S 2,4,11,21,31,110,124,185,279,399,716,1028,4552,6207,6543,11424,11557,

%T 12251,16199,23043,43390,155798,203095,457523,699782,865318,1294026,

%U 2918851,5635889,6459777,8999147,9213126,22383796,28194383,32131750,105097565,404165580

%N Where records occur in A001917.

%H Amiram Eldar, <a href="/A152597/b152597.txt">Table of n, a(n) for n = 1..47</a>

%F a(n) = A000720(A226216(n)). - _Amiram Eldar_, Nov 16 2023

%e 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.

%o (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;

%o (Python)

%o from itertools import islice

%o from sympy import nextprime, n_order

%o def agen():

%o     record, v, p = -1, 1, 3

%o     while True:

%o         if v > record: record = v; yield record

%o         v, p = (p-1)//n_order(2, p), nextprime(p)

%o print(list(islice(agen(), 20))) # _Michael S. Branicky_, Oct 09 2022

%Y 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.

%K nonn

%O 1,1

%A _Klaus Brockhaus_, Dec 09 2008

%E a(27)-a(37) from _Amiram Eldar_, Mar 08 2019