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 A250174 Numbers n such that Phi_14(n) is prime, where Phi is the cyclotomic polynomial. 21
 2, 3, 10, 11, 14, 15, 16, 17, 18, 21, 24, 25, 29, 37, 43, 44, 46, 49, 52, 54, 61, 66, 72, 73, 78, 84, 86, 87, 99, 101, 106, 114, 115, 128, 133, 135, 136, 143, 145, 148, 164, 169, 170, 173, 200, 219, 224, 226, 228, 231, 234, 240, 248, 255, 262, 275, 281, 282, 298, 301 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS n = 9069 * 2^64163 + 1 is an example of a rather large member of this sequence. The generated 115914 decimal digit prime is proved by the N-1 method (because n is prime and n*(n-1) is fully factored and this provides for an exactly 33.33...% factorization for Phi_14(n) - 1). - Serge Batalov, Mar 13 2015 LINKS Serge Batalov, Table of n, a(n) for n = 1..1595 EXAMPLE 2 is in the sequence because 2^6-2^5+2^4-2^3+2^2-2+1 = 43 which is prime. MATHEMATICA a250174[n_] := Select[Range[n], PrimeQ@Cyclotomic[14, #] &]; a250174 PROG (PARI) isok(n) = isprime(polcyclo(14, n)); \\ Michel Marcus, Mar 13 2015 CROSSREFS See A250177 for cross-references, A100330 (Phi_7(n) = n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 primes; these two sequences can also be considered an extension of each other into negative n values), A250177 (Phi_21(n) primes). Sequence in context: A146327 A344939 A278742 * A285622 A081706 A359251 Adjacent sequences: A250171 A250172 A250173 * A250175 A250176 A250177 KEYWORD nonn AUTHOR Eric Chen, Dec 24 2014 STATUS approved

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Last modified October 2 22:30 EDT 2023. Contains 365841 sequences. (Running on oeis4.)