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

Author

Jonas Kaiser, Nov 09 2017

Keywords

• nonn

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.

Crossrefs

Cf. A001133, A244626, A294717.

Programs

Mathematica

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

PARI

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