A372186 Numbers m such that 20*m + 1, 80*m + 1, 100*m + 1, and 200*m + 1 are all primes.

333, 741, 1659, 1749, 2505, 2706, 2730, 4221, 4437, 4851, 5625, 6447, 7791, 7977, 8229, 8250, 9216, 10833, 12471, 13950, 14028, 15147, 16002, 17667, 18207, 18246, 19152, 20517, 23400, 23421, 23961, 25689, 26247, 28587, 28608, 30363, 31584, 34167, 36330, 36378

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

Cf. A002997, A318646, A372189.

Similar sequences: A046025, A257035, A206024, A206349, A372187, A372188.

Sequence in context: A227228 A066801 A066349 * A043503 A202311 A319011

Adjacent sequences: A372183 A372184 A372185 * A372187 A372188 A372189

Keyword

nonn,easy

Author

Amiram Eldar, Apr 21 2024

Status

approved