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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).
2
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
1,1
COMMENTS
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.
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 *)
PROG
(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
(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
CROSSREFS
Cf. A001567. Subsequence of A295835.
Sequence in context: A289109 A247888 A243102 * A056086 A046012 A152952
KEYWORD
nonn
AUTHOR
Jonas Kaiser, Feb 09 2018
EXTENSIONS
More terms from Chai Wah Wu, Feb 10 2018
STATUS
approved