A297415 -id:A297415 - cp's OEIS frontend

A217465 Composite integers k such that 2^k == 2 (mod k*(k+1)).

561, 1905, 4033, 4681, 5461, 6601, 8481, 11305, 13741, 13981, 16705, 23377, 30121, 31417, 41041, 49141, 52633, 57421, 88357, 88561, 101101, 107185, 121465, 130561, 162193, 196021, 196093, 204001, 208465, 219781, 266305, 276013, 278545, 282133, 285541, 314821, 334153, 341497, 390937, 399001

Offset: 1

V. Raman, Oct 04 2012

nonn

Terms A019320(k) belongs to this sequence for k in A297415. - Max Alekseyev, Dec 29 2017

Amiram Eldar, Table of n, a(n) for n = 1..12766 (terms below 10^12; terms 1..100 from Harvey P. Dale)
Mersenne Forum, Prime Conjecture, 2012.

Subsequence of A216822.
Contains A303531 as a subsequence.
Cf. A019320, A217466, A217468, A297415, A298758.

Select[Range[400000],!PrimeQ[#]&&PowerMod[2,#,#(#+1)]==2&] (* Harvey P. Dale, Oct 12 2012 *)

for(n=1,10000,if((2^n)%(n*(n+1))==2&&isprime(n)==0,printf(n",")))

forcomposite(n=4,10^6, if(Mod(2,n*(n+1))^n==2, print1(n", "))) \\ Charles R Greathouse IV, Aug 29 2024

from sympy import isprime
A217465_list = [n for n in range(1,10**6) if pow(2,n,n*(n+1)) == 2 and not isprime(n)] # Chai Wah Wu, Mar 25 2021

A297414 Numbers k such that 2^m == 2 (mod m*(m+1)), where m = A019320(k).

Original entry on oeis.org

1, 4, 9, 12, 25, 36, 40, 52, 80, 92, 124, 150, 208, 306, 361, 630, 656, 1648, 1780, 2508, 3300, 3540, 5728, 6260, 6450, 7500, 10820, 12656, 14076, 14132, 18836, 20960, 23456, 24272, 35280, 43136

Offset: 1

Max Alekseyev, Dec 29 2017

nonn

Also, numbers k such that A019320(k) belongs to A216822.

Cf. A019320, A216822, A297413, A297415.

is_A297414(k) = my(m=polcyclo(k, 2)); Mod(2, m*(m+1))^m==2;

cp's OEIS Frontend

A217465 Composite integers k such that 2^k == 2 (mod k*(k+1)).

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A297414 Numbers k such that 2^m == 2 (mod m*(m+1)), where m = A019320(k).

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Comments

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PARI