A289257 Terms k of A006521 such that 2*k is a term of A124240.

1, 3, 9, 27, 81, 171, 243, 513, 729, 1539, 2187, 3249, 4617, 6561, 9747, 13203, 13851, 19683, 29241, 39609, 41553, 59049, 61731, 87723, 118827, 124659, 177147, 185193, 250857, 263169, 356481, 373977, 531441, 555579, 752571, 789507, 1063611, 1069443, 1121931, 1172889, 1594323, 1666737

Offset

1,2

Comments

Novák numbers n that are 2n Novák-Carmichael. See Kalmynin link.

Links

Table of n, a(n) for n=1..42.

Alexander Kalmynin, On Novák numbers, arXiv:1611.00417 [math.NT], 2016. See Theorem 7 p. 11.

Mathematica

Reap[Do[If[PowerMod[2, n, n]+1 == n && Divisible[2n, CarmichaelLambda[2n]], Print[n]; Sow[n]], {n, 2 10^6}]][[2, 1]] (* Jean-François Alcover, Sep 25 2018 *)

Prog

(PARI) isnov(n) = Mod(2, n)^n==-1; \\ A006521
isnovcar(n) = n%lcm(znstar(n)[2])==0; \\ A124240
isok(n) = isnov(n) && isnovcar(2*n);
(Python)
from itertools import count, islice
from sympy.ntheory.factor_ import reduced_totient
def A289257gen(): return filter(lambda n:2*n % reduced_totient(2*n) == 0 and pow(2, n, n)==n-1, count(1))
A289257_list = list(islice(A289257gen(), 20)) # Chai Wah Wu, Dec 11 2021

Crossrefs

Cf. A006521, A124240, A289258.

Sequence in context: A036143 A248960 A006521 * A014953 A274627 A080557

Adjacent sequences: A289254 A289255 A289256 * A289258 A289259 A289260

Keyword

nonn

Author

Michel Marcus, Jun 29 2017

Status

approved