login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A269769 Numbers of the form p^k - k where p is a prime number and k > 1. 2
2, 5, 7, 12, 23, 24, 27, 47, 58, 77, 119, 121, 122, 167, 238, 248, 287, 340, 359, 503, 527, 621, 723, 839, 959, 1014, 1328, 1367, 1679, 1847, 2037, 2180, 2194, 2207, 2397, 2807, 3120, 3479, 3719, 4084, 4487, 4910, 5039, 5327, 6239, 6553, 6856, 6887, 7919, 8179 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes of the form p^k - k where p is prime are 2, 5, 7, 23, 47, 167, 359, 503, ...

Subsequence of A057897.

A182474 is a subsequence.

Up to 10^14 all the terms have a unique representation as p^k - k. - Giovanni Resta, Mar 21 2017

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

    2 is a term because   2 = 2^2 - 2.

    5 is a term because   5 = 2^3 - 3.

    7 is a term because   7 = 3^2 - 2.

   12 is a term because  12 = 2^4 - 4.

  121 is a term because 121 = 2^7 - 7.

MAPLE

N:= 10000: # to get all terms <= N

P:= select(isprime, [$1..floor((N+2)^(1/2))]):

S:= {}:

for k from 2 do

  pmax:= floor((N+k)^(1/k));

  if pmax < 2 then break fi;

  S:= S union {seq(p^k-k, p = select(`<=`, P, pmax))};

od:

sort(convert(S, list)); # Robert Israel, Mar 21 2017

CROSSREFS

Cf. A000961, A057897, A182474.

Sequence in context: A333068 A029938 A213044 * A230428 A071013 A114727

Adjacent sequences:  A269766 A269767 A269768 * A269770 A269771 A269772

KEYWORD

nonn

AUTHOR

Altug Alkan, Mar 04 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 1 09:39 EDT 2022. Contains 354958 sequences. (Running on oeis4.)