A271842 -id:A271842 - cp's OEIS frontend

A272062 Positive numbers k such that k^2 - 1 divides 8^k - 1.

2, 4, 8, 10, 16, 22, 36, 40, 64, 96, 100, 196, 210, 256, 280, 316, 456, 560, 820, 1200, 1236, 1296, 1360, 1408, 1600, 1870, 2380, 2556, 3516, 3616, 4096, 4200, 4356, 5656, 6112, 6256, 6480, 8008, 8688, 10192, 10356, 11440, 11952, 12160, 13728, 14950, 16192, 17020, 19432, 21880, 22036

Offset: 1

Juri-Stepan Gerasimov, Apr 19 2016

nonn

From Robert Israel, Jun 08 2018: (Start)
All terms are even.
Are 2, 8 and 560 the only terms == 2 (mod 6)?  There are no others up to 3*10^9. (End)

			a(1) = 2 because (8^2 - 1)/(2^2 - 1) = 21.

Robert Israel, Table of n, a(n) for n = 1..2559

Cf. positive numbers n such that n^2 - 1 divides (2^k)^n - 1: A247219 (k=1), A271842 (k=2), this sequence (k=3).

[0] cat [n: n in [2..30000] | Denominator((8^n-1)/(n^2-1)) eq 1];

A272062:=n->`if`((8^n-1) mod (n^2-1) = 0, n, NULL): seq(A272062(n), n=2..5*10^4); # Wesley Ivan Hurt, Apr 21 2016

Select[Range[2, 22100], Divisible[8^# - 1, #^2 - 1] &] (* Michael De Vlieger, Apr 19 2016 *)

is(n)=Mod(8,n^2-1)^n==1 \\ Charles R Greathouse IV, Apr 19 2016

A281363 Smallest m>0 such that (2n)^2 - 1 divides (2^m)^(2n) - 1.

Original entry on oeis.org

1, 1, 2, 3, 3, 5, 6, 1, 4, 9, 3, 55, 90, 9, 14, 5, 30, 1, 18, 3, 10, 21, 6, 161, 84, 2, 130, 45, 9, 29, 30, 3, 2, 33, 11, 35, 90, 15, 5, 351, 27, 82, 28, 7, 22, 15, 90, 3, 120, 3, 50, 51, 6, 53, 18, 9, 154, 33, 12, 11, 110, 25, 50, 7, 7, 195, 18, 9, 34, 69

Offset: 1

Juri-Stepan Gerasimov, Apr 30 2016

nonn

			a(3) = 2 because (2*3)^2 - 1 = 35 divides (2^2)^(2*3) - 1 = 4095.

Giovanni Resta and Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms for n = 1..1000 from Giovanni Resta)

Cf. positive numbers n such that n^2 - 1 divides (2^k)^n - 1: A247219 (k=1), A271842 (k=2), A272062 (k=3).

Table[SelectFirst[Range@ 1200, Divisible[(2^#)^(2 n) - 1, (2 n)^2 - 1] &], {n, 84}] (* Michael De Vlieger, May 01 2016, Version 10 *)
a[n_] := Block[{m=1}, While[ PowerMod[2^m, 2*n, 4*n^2-1] != 1, m++]; m]; Array[a, 100] (* Giovanni Resta, May 05 2016 *)

def A281363(n):
    m, q = 1, 4*n**2-1
    p = pow(2, 2*n, q)
    r = p
    while r != 1:
        m += 1
        r = (r*p) % q
    return m # Chai Wah Wu, Jan 28 2017

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A272062 Positive numbers k such that k^2 - 1 divides 8^k - 1.

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A281363 Smallest m>0 such that (2n)^2 - 1 divides (2^m)^(2n) - 1.

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cp's OEIS Frontend

A272062 Positive numbers k such that k^2 - 1 divides 8^k - 1.

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Author

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Magma

Maple

Mathematica

PARI

A281363 Smallest m>0 such that (2*n)^2 - 1 divides (2^m)^(2*n) - 1.

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Mathematica

Python

A281363 Smallest m>0 such that (2n)^2 - 1 divides (2^m)^(2n) - 1.