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

Author

V. Raman, Oct 04 2012

Keywords

• nonn

Comments

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

Links

• 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.

Crossrefs

Subsequence of A216822.

Contains A303531 as a subsequence.

Cf. A019320, A217466, A217468, A297415, A298758.

Programs

Mathematica

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

PARI

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

PARI

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

Python

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