A372188 Numbers m such that 18*m + 1, 36*m + 1, 108*m + 1, and 162*m + 1 are all primes.
1, 71, 155, 176, 241, 346, 420, 540, 690, 801, 1145, 1421, 1506, 2026, 2066, 3080, 3235, 3371, 3445, 3511, 3640, 4746, 4925, 5681, 5901, 6055, 6520, 7931, 8365, 8970, 9006, 9556, 9685, 10186, 11396, 11750, 11935, 12055, 12666, 13205, 13266, 13825, 13881, 14606
Offset: 1
Examples
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.
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.
Crossrefs
Programs
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Mathematica
q[n_] := AllTrue[{18, 36, 108, 162}, PrimeQ[#*n + 1] &]; Select[Range[15000], q] -
PARI
is(n) = isprime(18*n + 1) && isprime(36*n + 1) && isprime(108*n + 1) && isprime(162*n + 1);
Comments