OFFSET
1,1
COMMENTS
There are no composite numbers up to 2*10^17. The first composite term is 229467972529064957.
LINKS
Jonas Kaiser, On the relationship between the Collatz conjecture and Mersenne prime numbers, arXiv:1608.00862 [math.GM], 2016.
MAPLE
a:=k->`if`(k mod 120 = 77 and (2*k-1)*2^((k-1)/2) mod k = 1 and (2*k-1)*3^((k-1)/2) mod k = 1 and (2*k-1)*5^((k-1)/2) mod k = 1, k, NULL): seq(a(k), k=1..50); # Muniru A Asiru, Mar 11 2018
MATHEMATICA
k = 77; lst = {}; While[k < 12000, If[Mod[(2k -1) PowerMod[{2, 3, 5}, (k -1)/2, k], k] == {1, 1, 1}, AppendTo[lst, k]]; k += 120]; lst (* Robert G. Wilson v, Feb 13 2018 *)
PROG
(PARI) is(n) = n%120==77 &&(2*n-1)* Mod(2, n)^((n-1)\2)==1 &&(2*n-1)* Mod(3, n)^((n-1)\2)==1 &&(2*n-1)* Mod(5, n)^((n-1)\2)==1 \\
(GAP) Filtered([1..11000], k->k mod 120 = 77 and (2*k-1)*2^((k-1)/2) mod k = 1 and (2*k-1)*3^((k-1)/2) mod k = 1 and (2*k-1)*5^((k-1)/2) mod k = 1); # Muniru A Asiru, Mar 11 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonas Kaiser, Feb 11 2018
STATUS
approved