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

1,2

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

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

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.

Mathematica

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

Prog

(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
(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

Crossrefs

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

Sequence in context: A130002 A320812 A162034 * A295616 A059929 A123029

Adjacent sequences: A105283 A105284 A105285 * A105287 A105288 A105289

Keyword

nonn

Author

Zak Seidov, Apr 25 2005

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

Status

approved