The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A294187 Numbers k == 77 (mod 120) such that (2*k-1)*2^((k-1)/2), (2*k-1)*3^((k-1)/2) and (2*k-1)*5^((k-1)/2) are congruent to 1 (mod k). 0
 197, 317, 557, 677, 797, 1277, 1637, 1877, 1997, 2237, 2357, 2477, 2837, 2957, 3557, 3677, 3797, 3917, 4157, 4397, 4517, 4637, 4877, 5237, 5477, 5717, 6197, 6317, 6917, 7517, 7757, 7877, 8117, 8237, 8597, 8837, 9437, 9677, 10037 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A001567. Sequence in context: A142121 A142274 A142624 * A158223 A142503 A142568 Adjacent sequences:  A294184 A294185 A294186 * A294188 A294189 A294190 KEYWORD nonn AUTHOR Jonas Kaiser, Feb 11 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 21 08:18 EDT 2021. Contains 345358 sequences. (Running on oeis4.)