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A034922 Numbers n such that 17^n-16 is prime. 1
11, 21, 127, 149, 469, 2019 (list; graph; refs; listen; history; text; internal format)



Related to hyperperfect numbers of a certain form.

Contribution 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.


The next terms are > 4000. - Vincenzo Librandi, Sep 27 2012


Daniel Minoli, W. Nakamine, Mersenne Numbers Rooted On 3 For Number Theoretic Transforms, 1980 IEEE International Conf. on Acoust., Speech and Signal Processing. [From Daniel Minoli (daniel.minoli(AT)ses.com), Aug 27 2009]

Daniel Minoli, Voice over MPLS, McGraw-Hill, New York, NY, 2002, ISBN 0-07-140615-8 (p.114-134) [From Daniel Minoli (daniel.minoli(AT)ses.com), Aug 27 2009]

Daniel Minoli, Robert Bear, Hyperperfect Numbers, PME (Pi Mu Epsilon) Journal, University Oklahoma, Fall 1975, pp. 153-157. [From Daniel Minoli (daniel.minoli(AT)ses.com), Aug 27 2009]


Table of n, a(n) for n=1..6.

J. S. McCranie, A study of hyperperfect numbers, J. Int. Seqs. Vol. 3 (2000) #P00.1.3


Select[Range[3000], PrimeQ[17^# - 16] &] (* Vincenzo Librandi, Sep 27 2012 *)


Sequence in context: A166707 A116525 A094623 * A015446 A254208 A083177

Adjacent sequences:  A034919 A034920 A034921 * A034923 A034924 A034925




Jud McCranie


a(6) from Vincenzo Librandi, Sep 27 2012



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Last modified November 27 03:20 EST 2015. Contains 264523 sequences.