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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 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 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 Cf. A002997, A126797, A318646. Similar sequences: A046025, A257035, A206024, A206349, A372186, A372188. Sequence in context: A020322 A055829 A243801 * A093295 A060484 A017811 Adjacent sequences: A372184 A372185 A372186 * A372188 A372189 A372190 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.)