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A034922
Numbers k such that 17^k - 16 is prime.
1
11, 21, 127, 149, 469, 2019, 13953, 21689, 25679
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(8)=21689 and a(9)=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
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
KEYWORD
nonn,more
AUTHOR
EXTENSIONS
a(6) from Vincenzo Librandi, Sep 27 2012
a(8) and a(9) from Andrej Jakobcic, Feb 17 2019
a(7) inserted by Michael S. Branicky, Jun 09 2024
STATUS
approved