cp's OEIS Frontend

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).

%I A294092 #40 Sep 06 2024 08:07:09
%S A294092 239,359,479,599,719,839,1319,1439,1559,2039,2399,2879,2999,3119,3359,
%T A294092 3719,4079,4679,4799,4919,5039,5279,5399,5519,5639,5879,6359,6599,
%U A294092 6719,6959,7079,7559,7919,8039,8999,9239,9479,9719,9839,10079,10559,10799,11159,11279
%N 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).
%C A294092 So far no composite numbers have been found in this sequence. There are no pseudoprimes up to 2^64 in this sequence, so a composite term in this sequence has to exceed 18446744066047760377.
%H A294092 Chai Wah Wu, <a href="/A294092/b294092.txt">Table of n, a(n) for n = 1..10000</a>
%H A294092 Jonas Kaiser, <a href="https://arxiv.org/abs/1608.00862">On the relationship between the Collatz conjecture and Mersenne prime numbers</a>, arXiv:1608.00862 [math.GM], 2016.
%t A294092 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 *)
%o A294092 (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
%o A294092 (Python)
%o A294092 A294092_list, k, m = [], 119, 59
%o A294092 while len(A294092_list) < 10000:
%o A294092     if pow(2,m,k) == 1 and pow(3,m,k) == 1 and pow(5,m,k) == 1:
%o A294092         A294092_list.append(k)
%o A294092     k += 120
%o A294092     m += 60 # _Chai Wah Wu_, Feb 09 2018
%o A294092 (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
%Y A294092 Cf. A001567. Subsequence of A295835.
%K A294092 nonn
%O A294092 1,1
%A A294092 _Jonas Kaiser_, Feb 09 2018
%E A294092 More terms from _Chai Wah Wu_, Feb 10 2018