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 A066180 a(n) = smallest base b so that repunit (b^prime(n) - 1) / (b - 1) is prime, where prime(n) = n-th prime; or 0 if no such base exists. 12
 2, 2, 2, 2, 5, 2, 2, 2, 10, 6, 2, 61, 14, 15, 5, 24, 19, 2, 46, 3, 11, 22, 41, 2, 12, 22, 3, 2, 12, 86, 2, 7, 13, 11, 5, 29, 56, 30, 44, 60, 304, 5, 74, 118, 33, 156, 46, 183, 72, 606, 602, 223, 115, 37, 52, 104, 41, 6, 338, 217, 13, 136, 220, 162, 35, 10, 218, 19, 26, 39 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Is a(n) = 0 possible? Let p be the n-th prime; Cp(x) be the p-th cyclotomic polynomial (x^p - 1)/(x - 1); a(n) is the least k > 1 such that Cp(k) is prime. The values associated with a(5) and a(8) through a(70) have been certified prime with Primo. (a(1) through a(4), a(6) and a(7) give prime(2), prime(4), prime(11), prime(31), prime(1028) and prime(12251), respectively.) REFERENCES Paulo Ribenboim, "The New Book of Prime Numbers Records", Springer, 1996, p. 353. LINKS Robert G. Wilson v, Table of n, a(n) for n = 1..300 (terms 1..200 from Charles R Greathouse IV). H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930. Andy Steward, Titanic Prime Generalized Repunits. Eric Weisstein's World of Mathematics, Repunit (World of Mathematics). H. C. Williams & E. Seah, Some primes of the form: (a^n - 1)/(a - 1), Mathematics of Computation 23, 1979. FORMULA a(n) = A085398(prime(n)). EXAMPLE a(5) = 5 because 11 is the 5th prime; (b^5 - 1)/(b - 1) is composite for b = 2,3,4 and prime ((5^11 - 1)/4 = 12207031) for b = 5. b = 61 for prime(12) = 37 because (61^37 - 1)/60 is prime and 61 is the least base b that makes (b^37 - 1)/(b - 1) a prime. MATHEMATICA Table[p = Prime[n]; b = 1; While[b++; ! PrimeQ[(b^p - 1)/(b - 1)]]; b, {n, 1, 70}] (* Lei Zhou, Oct 07 2011 *) PROG (PARI) /* This program assumes (probable) primes exist for each n. */ /* All 70 (probable) primes found by this program have been proved prime. */ gen_repunit(b, n) = (b^prime(n)-1)/(b-1); for(n=1, 70, b=1; until(isprime(p), b++; p=gen_repunit(b, n)); print1(b, ", ")); CROSSREFS Cf. A004023 (prime repunits in base 10), A000043 (prime repunits in base 2, Mersenne primes), A055129 (table of repunits). Cf. A084732, A085398. Sequence in context: A103512 A130086 A084731 * A123487 A130325 A154097 Adjacent sequences:  A066177 A066178 A066179 * A066181 A066182 A066183 KEYWORD nonn AUTHOR Frank Ellermann, Dec 15 2001 EXTENSIONS Sequence extended to 16 terms by Don Reble, Dec 18 2001 More terms from Rick L. Shepherd, Sep 14 2002 Entry revised by N. J. A. Sloane, Jul 23 2006 STATUS approved

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Last modified May 26 14:57 EDT 2020. Contains 334626 sequences. (Running on oeis4.)