OFFSET
1,2
COMMENTS
If m is a term, then (18*m + 1) * (36*m + 1) * (108*m + 1) * (162*m + 1) is a Carmichael number (A002997). These are the Carmichael numbers of the form W_4(3*m) in Nakamula et al. (2007).
The corresponding Carmichael numbers are 12490201, 288503529142321, 6548129556412321, ...
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Ken Nakamula, Hirofumi Tsumura, and Hiroaki Komai, New polynomials producing absolute pseudoprimes with any number of prime factors, arXiv:math/0702410 [math.NT], 2007.
EXAMPLE
1 is a term since 18*1 + 1 = 19, 36*1 + 1 = 37, 108*1 + 1 = 109, and 162*1 + 1 = 163 are all primes.
71 is a term since 18*71 + 1 = 1279, 36*71 + 1 = 2557, 108*71 + 1 = 7669, and 162*71 + 1 = 11503 are all primes.
MATHEMATICA
q[n_] := AllTrue[{18, 36, 108, 162}, PrimeQ[#*n + 1] &]; Select[Range[15000], q]
PROG
(PARI) is(n) = isprime(18*n + 1) && isprime(36*n + 1) && isprime(108*n + 1) && isprime(162*n + 1);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Apr 21 2024
STATUS
approved