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A372187 Numbers m such that 72*m + 1, 576*m + 1, 648*m + 1, 1296*m + 1, and 2592*m + 1 are all primes. 4
95, 890, 3635, 8150, 9850, 12740, 13805, 18715, 22590, 23591, 32526, 36395, 38571, 49016, 49456, 57551, 58296, 61275, 80756, 81050, 84980, 99940, 104346, 115361, 116761, 121055, 122550, 129320, 140331, 142625, 149431, 153505, 159306, 159730, 169625, 173485, 181661 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
If m is a term, then (72*m + 1) * (576*m + 1) * (648*m + 1) * (1296*m + 1) * (2592*m + 1) is a Carmichael number (A002997). These are the Carmichael numbers of the form U_{5,5}(m) in Nakamula et al. (2007).
The corresponding Carmichael numbers are 698669495582067436250881, 50411423376758357271937215361, 57292035175893741987253427965441, ...
LINKS
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
95 is a term since 72*95 + 1 = 6841, 576*95 + 1 = 54721, 648*95 + 1 = 61561, 1296*95 + 1 = 123121, and 2592*95 + 1 = 246241 are all primes.
MATHEMATICA
q[n_] := AllTrue[{72, 576, 648, 1296, 2592}, PrimeQ[#*n + 1] &]; Select[Range[200000], q]
PROG
(PARI) is(n) = isprime(72*n + 1) && isprime(576*n + 1) && isprime(648*n + 1) && isprime(1296*n + 1) && isprime(2592*n + 1);
CROSSREFS
Similar sequences: A046025, A257035, A206024, A206349, A372186, A372188.
Sequence in context: A020322 A055829 A243801 * A093295 A060484 A017811
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Apr 21 2024
STATUS
approved

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Last modified July 22 15:01 EDT 2024. Contains 374501 sequences. (Running on oeis4.)