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 A246121 Least k such that k^(6^n)*(k^(6^n)-1)+1 is prime. 3
 2, 3, 88, 28, 688, 7003, 1925 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Numbers of the form k^m*(k^m-1)+1 with m > 0, k > 1 may be primes only if m is 3-smooth, because these numbers are Phi(6,k^m) and cyclotomic factorizations apply to any prime divisors >3. This series is a subset of A205506 with only m=6^n. Numbers of this form are Generalized unique primes. a(6) generates a 306477-digit prime. LINKS C.Caldwell, Generalized unique primes EXAMPLE When k = 88, k^72-k^36+1 is prime. Since this isn't prime for k < 88, a(2) = 88. PROG (PARI) a(n)=k=1; while(!ispseudoprime(k^(6^n)*(k^(6^n)-1)+1), k++); k n=0; while(n<100, print1(a(n), ", "); n++) CROSSREFS Cf. A205506, A246119, A246120, A153438, A101406, A153436, A056993. Sequence in context: A153228 A041401 A103013 * A224934 A299691 A042901 Adjacent sequences:  A246118 A246119 A246120 * A246122 A246123 A246124 KEYWORD nonn,more,hard AUTHOR Serge Batalov, Aug 14 2014 EXTENSIONS a(6) from Serge Batalov, Aug 15 2014 STATUS approved

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Last modified January 17 03:14 EST 2021. Contains 340214 sequences. (Running on oeis4.)