A034922 Numbers k such that 17^k - 16 is prime.

11, 21, 127, 149, 469, 2019, 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(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

Table of n, a(n) for n=1..8.

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

Jud McCranie

Extensions

a(6) from Vincenzo Librandi, Sep 27 2012

a(7) and a(8) from Andrej Jakobcic, Feb 17 2019

Status

approved