A293394 Numbers k such that (2*k-1)*(2^((k-1)/4)) == 1 (mod k).

1, 17, 41, 97, 137, 193, 241, 313, 401, 409, 433, 449, 457, 521, 569, 641, 673, 761, 769, 809, 857, 929, 953, 977, 1009, 1129, 1297, 1321, 1361, 1409, 1489, 1657, 1697, 1873, 1993, 2017, 2081, 2137, 2153, 2161

Offset

1,2

Comments

It appears that many elements of this sequence are prime. The first "pseudoprime" in this sequence is 74665.

Links

Charles R Greathouse IV, 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.

Mathematica

Select[Range[1, 3001, 4], #==1 || Mod[-PowerMod[#-2, (#-1)/4, #], #]==1&] (* Jean-François Alcover, Nov 18 2018 *)

Prog

(PARI) is(n)=n%4==1 && (2*n-1)*Mod(2, n)^(n>>2)==1 \\ Charles R Greathouse IV, Nov 09 2017

Crossrefs

Cf. A001133, A244626, A294717.

Sequence in context: A158014 A139879 A281792 * A070179 A155072 A243451

Adjacent sequences: A293391 A293392 A293393 * A293395 A293396 A293397

Keyword

nonn

Author

Jonas Kaiser, Nov 09 2017

Status

approved