OFFSET
1,1
COMMENTS
If m is a term, then (20*m + 1) * (80*m + 1) * (100*m + 1) * (200*m + 1) is a Carmichael number (A002997). These are the Carmichael numbers of the form U_{4,4}(m) in Nakamula et al. (2007).
The corresponding Carmichael numbers are 393575432565765601, 9648687289456956001, 242412946401534283201, ...
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
333 is a term since 20*333 + 1 = 6661, 80*333 + 1 = 26641, 100*333 + 1 = 33301, and 200*333 + 1 = 66601 are all primes.
MATHEMATICA
q[n_] := AllTrue[{20, 80, 100, 200}, PrimeQ[# * n + 1] &]; Select[Range[40000], q]
PROG
(PARI) is(n) = isprime(20*n + 1) && isprime(80*n + 1) && isprime(100*n + 1) && isprime(200*n + 1);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Apr 21 2024
STATUS
approved