The On-Line Encyclopedia of Integer Sequences (OEIS)

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A128338

Numbers k such that (8^k + 5^k)/13 is prime.
(history; published version)

#10 by Jon E. Schoenfield at Thu Nov 01 21:25:43 EDT 2018

STATUS

editing

approved

#9 by Jon E. Schoenfield at Thu Nov 01 21:25:41 EDT 2018

NAME

Numbers n k such that (8^n k + 5^nk)/13 is prime.

COMMENTS

a(8) > 10^5 . - _Robert Price, _, Jan 21 2013

STATUS

approved

editing

#8 by Charles R Greathouse IV at Fri Feb 17 12:04:37 EST 2017

STATUS

editing

approved

#7 by Charles R Greathouse IV at Fri Feb 17 12:03:56 EST 2017

PROG

(PARI) is(n)=isprime((8^n+5^n)/13) \\ Charles R Greathouse IV, Feb 17 2017

STATUS

approved

editing

#6 by Joerg Arndt at Mon Jan 21 10:45:49 EST 2013

STATUS

proposed

approved

#5 by Robert Price at Mon Jan 21 10:28:29 EST 2013

STATUS

editing

proposed

Discussion

Mon Jan 21

10:33

Alois P. Heinz: Is the first comment still true? Is a(7) prime or only probable prime?

10:48

Robert Price: I read the first comment as the terms themselves are prime. 7, 19, 167...21647 are prime.  Generally a(n) values greater than n=1000 are probable primes.  Perhaps a project to delineate which are proven and which are probable is in order for primes in the OEIS?

#4 by Robert Price at Mon Jan 21 10:27:56 EST 2013

DATA

7, 19, 167, 173, 223, 281, 21647

COMMENTS

a(8) > 10^5 - Robert Price, Jan 21 2013

EXTENSIONS

a(7) from Robert Price, Jan 21 2013

STATUS

approved

editing

#3 by Russ Cox at Sat Mar 31 13:20:35 EDT 2012

AUTHOR

_Alexander Adamchuk (alex(AT)kolmogorov.com), _, Feb 27 2007

Discussion

Sat Mar 31

13:20

OEIS Server: https://oeis.org/edit/global/879

#2 by N. J. A. Sloane at Sat Nov 10 03:00:00 EST 2007

COMMENTS

All terms are primeprimes.

KEYWORD

hard,more,nonn,new

#1 by N. J. A. Sloane at Fri May 11 03:00:00 EDT 2007

NAME

Numbers n such that (8^n + 5^n)/13 is prime.

DATA

7, 19, 167, 173, 223, 281

OFFSET

1,1

COMMENTS

All terms are prime.

MATHEMATICA

k=8; Do[p=Prime[n]; f=(k^p+5^p)/(k+5); If[ PrimeQ[f], Print[p] ], {n, 1, 100}]

CROSSREFS

Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128339, A128340, A128341, A128342, A128343. Cf. A004061, A082182, A121877, A059802. Cf. A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.

KEYWORD

hard,more,nonn

AUTHOR

Alexander Adamchuk (alex(AT)kolmogorov.com), Feb 27 2007

STATUS

approved