A294092 Numbers k == 119 (mod 120) such that 2^((k-1)/2), 3^((k-1)/2) and 5^((k-1)/2) are congruent to 1 (mod k).
239, 359, 479, 599, 719, 839, 1319, 1439, 1559, 2039, 2399, 2879, 2999, 3119, 3359, 3719, 4079, 4679, 4799, 4919, 5039, 5279, 5399, 5519, 5639, 5879, 6359, 6599, 6719, 6959, 7079, 7559, 7919, 8039, 8999, 9239, 9479, 9719, 9839, 10079, 10559, 10799, 11159, 11279
Offset: 1
Keywords
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10000
- Jonas Kaiser, On the relationship between the Collatz conjecture and Mersenne prime numbers, arXiv:1608.00862 [math.GM], 2016.
Programs
-
GAP
Filtered([1..14000],n->n mod 120=119 and 2^((n-1)/2) mod n =1 and 3^((n-1)/2) mod n =1 and 5^((n-1)/2) mod n =1); # Muniru A Asiru, Feb 15 2018
-
Mathematica
k = 119; lst = {}; While[k < 12000, If[ PowerMod[{2, 3, 5}, (k - 1)/2, k] == {1, 1, 1}, AppendTo[lst, k]]; k += 120]; lst (* Robert G. Wilson v, Feb 11 2018 *) -
PARI
is(n) = n%120==119 && Mod(2, n)^((n-1)\2)==1 && Mod(3, n)^((n-1)\2)==1 && Mod(5, n)^((n-1)\2)==1
-
Python
A294092_list, k, m = [], 119, 59 while len(A294092_list) < 10000: if pow(2,m,k) == 1 and pow(3,m,k) == 1 and pow(5,m,k) == 1: A294092_list.append(k) k += 120 m += 60 # Chai Wah Wu, Feb 09 2018
Extensions
More terms from Chai Wah Wu, Feb 10 2018
Comments