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 A034922 Numbers k such that 17^k - 16 is prime. 1
 11, 21, 127, 149, 469, 2019, 21689, 25679 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Related to hyperperfect numbers of a certain form. From Daniel Minoli (daniel.minoli(AT)ses.com), Aug 27 2009: (Start) Minoli defined the sequences and concepts that follow in the 1980 IEEE paper below: - For t=2 to infinity, the sequence m(n,t) = n exp(t) - (n-1) is called a Mersenne Sequence Rooted on n - If n is prime, this sequence is called a Legitimate Mersenne Sequence - Any j belonging to the sequence m(n,t) is called a Generalized Mersenne Number (n-GMN) - If j belonging to the sequence m(n,t) is prime, it is then called a n-Generalized Mersenne Prime (n-GMP). Note: m(n,t) = n*m(n,t-1) + n exp(2) - 2*n+1. These numbers play a role in the context of hyperperfect numbers. (End) The next terms are > 4000. - Vincenzo Librandi, Sep 27 2012 a(7)=21689 and a(8)=25679 correspond to probable primes, found with Dario Alpern's factorization tool using the elliptic curve method; no more terms < 35000. - Andrej Jakobcic, Feb 17 2019 REFERENCES Daniel Minoli, Voice over MPLS, McGraw-Hill, New York, NY, 2002, ISBN 0-07-140615-8 (pp. 114-134). LINKS Dario Alejandro Alpern, Factorization using the Elliptic Curve Method J. S. McCranie, A study of hyperperfect numbers, J. Int. Seqs. Vol. 3 (2000) #P00.1.3. Daniel Minoli and Robert Bear, Hyperperfect Numbers, Pi Mu Epsilon Journal, Fall 1975, pp. 153-157. Daniel Minoli, W. Nakamine, Mersenne Numbers Rooted On 3 For Number Theoretic Transforms, 1980 IEEE International Conf. on Acoust., Speech and Signal Processing. MATHEMATICA Select[Range[3000], PrimeQ[17^# - 16] &] (* Vincenzo Librandi, Sep 27 2012 *) PROG (PARI) isok(n) = isprime(17^n-16); \\ Michel Marcus, Mar 11 2016 CROSSREFS Sequence in context: A116525 A094623 A321509 * A015446 A254208 A083177 Adjacent sequences:  A034919 A034920 A034921 * A034923 A034924 A034925 KEYWORD nonn,more AUTHOR EXTENSIONS a(6) from Vincenzo Librandi, Sep 27 2012 a(7) and a(8) from Andrej Jakobcic, Feb 17 2019 STATUS approved

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Last modified October 16 11:11 EDT 2019. Contains 328056 sequences. (Running on oeis4.)