A152598 -id:A152598 - cp's OEIS frontend

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

Klaus Brockhaus, Dec 09 2008

nonn

			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.

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

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.

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;

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

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

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

A226216 Primes p such that (p-1)/ord(2,p) > (q-1)/ord(2,q) for odd primes q < p.

Original entry on oeis.org

3, 7, 31, 73, 127, 601, 683, 1103, 1801, 2731, 5419, 8191, 43691, 61681, 65537, 121369, 122921, 131071, 178481, 262657, 524287, 2099863, 2796203, 6700417, 10567201, 13264529, 20394401, 48544121, 97685839, 112901153, 160465489, 164511353, 420778751, 536903681, 616318177

Offset: 1

Charles R Greathouse IV, May 31 2013

nonn

Essentially records in A001917. Sequence is infinite.

The Mersenne primes (A000668) are a subset. - Jeppe Stig Nielsen, Aug 30 2015

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

Cf. A000668, A001917, A014664, A152597, A152598.

r=0; p=3; L={}; While[Length@L < 20, v = (p-1)/ MultiplicativeOrder[2, p]; If[v > r, r = v; AppendTo[L, p]]; p = NextPrime@ p]; L (* Giovanni Resta, Aug 31 2015 *)

r=0;forprime(p=3,1e9,t=(p-1)/znorder(Mod(2,p));if(t>r,r=t;print1(p", ")))

a(n) = prime(A152597(n)). - Amiram Eldar, Nov 16 2023

A182109 Records in A094593.

Original entry on oeis.org

1, 2, 4, 5, 6, 12, 16, 39, 84, 156, 350, 358, 589, 984, 2030, 2682, 3312, 4364, 19152, 61320, 61632, 142066, 353998, 702794, 1063044, 2056526, 2866334, 5479152, 8751462, 43544486

Offset: 1

Vassilis Papadimitriou, Apr 12 2012

It is for A094593 what A152598 is for A001917.

			First few terms of A094593 are 1, 1, 2, 4, 1, 1, 2, 1, 1, 2, 5, 1, 2, 1, 2, 6, 3, 2, 6, 1, 2, 1, 2, 1, 3, 2, 4, 1, 1, 2, 1, 1, 1, 3, 2, 1, 2, 1, 2, 4, 2, 12, so a(1) to a(6) are 1, 2, 4, 5, 6, 12.

Cf. A094593.

a(26)-a(30) from Chai Wah Wu, Jan 15 2020

A174437 Successive maximal values of A174435.

Original entry on oeis.org

1, 2, 3, 4, 9, 10, 16, 31, 36, 48, 105, 129, 315, 316, 387, 538, 1285, 1542, 2048, 3855, 4599, 4864, 7760, 13797, 18166, 24417, 60787, 104694

Offset: 1

Vassilis Papadimitriou, Mar 19 2010

			First terms of A174435 are: 1,1,1,1,1,2,1,1,1,1,1,2,1,1,3,1,1,1,2,2,3,1,1,1,1,3,1,2,1,1,1,2,1,1,2,1,1,3,2,4,2,1,1,1,1,1,1,1,4,2,2,1,1,1,1,1,1,1,1,2,3,2,1,4,3,1,2,1,1,9, so a(1)=1, a(2)=2, a(3)=3, a(4)=4, a(5)=9.

It is for A174435 what A152598 is for A001917.

cp's OEIS Frontend

A152597 Where records occur in A001917.

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A226216 Primes p such that (p-1)/ord(2,p) > (q-1)/ord(2,q) for odd primes q < p.

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A182109 Records in A094593.

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A174437 Successive maximal values of A174435.

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