A105286 Numbers k such that prime(k+1) == 1 (mod k).

1, 2, 3, 10, 24, 25, 66, 168, 182, 186, 187, 188, 438, 6462, 40071, 40084, 40085, 40091, 40108, 40118, 251745, 637224, 637306, 637336, 637338, 10553441, 10553445, 10553452, 10553479, 10553515, 10553550, 10553829, 27067032, 27067054, 27067134, 69709710, 69709713, 179992838, 179993008, 3140421868, 8179002150, 55762149074, 1003652347080, 1003652347109, 1003652347112, 1003652347352, 1003652347375

Offset: 1

Author

Zak Seidov, Apr 25 2005

Keywords

• nonn

Comments

If k is a term, then prime(k+1)^prime(k+1) is a reverse Meertens number in base prime(k+1)^((prime(k+1)-1)/k). - Chai Wah Wu, Dec 14 2022

Integers k such that A004649(k+1) = 1. - Michel Marcus, Dec 30 2022

Links

• Chai Wah Wu, Meertens Number and Its Variations, arXiv:1603.08493 [math.NT], 2016.
• Chai Wah Wu, Meertens number and its variations, Communications on Number Theory and Combinatorial Theory, 3 (2022), article 5.

Crossrefs

Cf. A004649, A105287, A105288, A105290, A105329, A105451.

Programs

Mathematica

bb={};Do[If[1==Mod[Prime[n+1], n], bb=Append[bb, n]], {n, 1, 200000}];bb

Python

from itertools import count, islice
from sympy import prime
def A105286_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda k: not (prime(k+1)-1)%k,count(max(startvalue,1)))
A105286_list = list(islice(A105286_gen(),10)) # Chai Wah Wu, Dec 14 2022

Sage

def A105286(max) :
    terms = []
    p = 3
    for n in range(1, max+1) :
        if (p - 1) % n == 0 : terms.append(n)
        p = next_prime(p)
    return terms
# Eric M. Schmidt, Feb 05 2013

Extensions

More terms from Farideh Firoozbakht, May 12 2005

First term inserted by Eric M. Schmidt, Feb 05 2013

More terms from Michel Marcus, Dec 29 2022

a(40)-a(47) from Max Alekseyev, Aug 31 2024