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
Keywords
Links
- Alexander Kalmynin, On Novák numbers, arXiv:1611.00417 [math.NT], 2016. See Theorem 7 p. 11.
Programs
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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 *) -
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);
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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
Comments