A242865 -id:A242865 - cp's OEIS frontend

A276671 Positive integers k such that 3^k == 2 (mod k).

1, 2929, 9742277641, 23341869101, 15092205901438895, 16311037042239935

Offset: 1

Max Alekseyev, Oct 05 2016

No other terms below 2*10^16. A larger term: 31744873758348589012852097851.

Cf. A015973, A067945, A015949, A055686, A242865, A234535, A234536, A050259.

Join[{1}, Select[Range[10000], PowerMod[3, #, #] == 2 &]] (* Alonso del Arte, Oct 11 2016 *)

isok(n) = Mod(3, n)^n == Mod(2, n); \\ Dmitry Ezhov, Sep 28 2016

Order of terms corrected by Felix Fröhlich, Oct 06 2016

a(5)-a(6) from Sergey Paramonov, Oct 03 2021

A277344 3-Knödel numbers (A033553) that are not divisible by 3.

Original entry on oeis.org

50963, 5834755, 9835843, 155627923, 245056003, 332852435, 556268443, 724014203, 795650963, 831912763, 2440444163, 4080848203, 5067702643, 5140068643, 5555216803, 7461332483, 8438160643, 11766788323, 11951765003, 13058213003, 13483943203, 14528402983, 16644521435, 17847852803

Offset: 1

Max Alekseyev, Oct 09 2016

nonn

Max Alekseyev, Table of n, a(n) for n = 1..775 (all terms below 10^16)

Intersection of A033553 and A242865.
Intersection of A033553 and A130133.
Subsequence of A015922.

A346988 a(n) is the smallest k > n such that n^(k-n) == 1 (mod k).

Original entry on oeis.org

2, 20737, 9299, 7, 13, 311, 15, 127, 17, 37, 14, 23, 17, 157, 106, 31, 29, 312953, 45, 95951, 41, 91, 33, 47, 28, 95, 35, 271, 35, 9629, 39, 311, 85, 397, 46, 71, 43, 1793, 95, 79, 61, 821, 51, 18881, 67, 103, 51, 12409, 73, 409969, 65, 87, 65, 71233, 63, 155, 65, 69, 87, 1962251, 91, 2443783, 155

Offset: 1

Thomas Ordowski, Aug 10 2021

nonn

Smallest k > n coprime to n such that n^k == n^n (mod k).

If a(n) is a prime p, then n^(n-1) == 1 (mod p).

Chai Wah Wu, Table of n, a(n) for n = 1..1000

Cf. A173572, A242865, A344681.

a[n_] := Module[{k = n + 1}, While[PowerMod[n, k - n, k] != 1, k++]; k]; Array[a, 60] (* Amiram Eldar, Aug 10 2021 *)

a(n) = my(k=n+1); while (Mod(n, k)^(k-n) != 1, k++); k; \\ Michel Marcus, Aug 10 2021

def A346988(n):
    k, kn = n+1, 1
    while True:
        if pow(n,kn,k) == 1:
            return k
        k += 1
        kn += 1 # Chai Wah Wu, Aug 28 2021

More terms from Amiram Eldar, Aug 10 2021

cp's OEIS Frontend

A276671 Positive integers k such that 3^k == 2 (mod k).

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A277344 3-Knödel numbers (A033553) that are not divisible by 3.

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A346988 a(n) is the smallest k > n such that n^(k-n) == 1 (mod k).

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Author

Keywords

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Mathematica

PARI

Python

Extensions