login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A285886 Primes of the form (1 + x)^y + (-x)^y where x is a divisor of y. 5
5, 7, 13, 17, 31, 37, 97, 127, 257, 881, 4651, 8191, 65537, 131071, 524287, 1273609, 2147483647, 2305843009213693951, 618970019642690137449562111, 3512911982806776822251393039617, 162259276829213363391578010288127, 170141183460469231731687303715884105727 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If x = y then: 13, 37, 881, 4651, 1273609, ...

Primes of the form (1 + x)^y - x^y where y is divisor of x: 3, 5, 7, 31, 37, 127, 4651, 8191, 131071, 524287, ..., which is A285887.

LINKS

Georg Fischer, Table of n, a(n) for n = 1..23

J. S. Gerasimov, x^(y + 1) - y^x, SeqFan list, Aug 18 2014.

EXAMPLE

5 is in this sequence because (1 + 1)^2 + (-1)^2 = 5 is prime where 1 is a divisor of 2.

A complete list of (x, y, p) corresponding to the shown data is

  (1,2,5), (1,3,7), (2,2,13), (1,4,17), (1,5,31), (3,3,37), (2,4,97),(1,7,127), (1,8,257), (4,4,881), (5,5,4651), (1,13,8191), (1,16,65537),

  (1,17,131071), (1,19,524287), (7,7,1273609), (1,31,2147483647),

  (1,61,2305843009213693951), (1,89,618970019642690137449562111),

  (8,32,3512911982806776822251393039617),

  (1,107,162259276829213363391578010288127),

  (1,127,170141183460469231731687303715884105727).

  Further terms correspond to (x,y) = {(1,521), (1,607), (167,167), (1,1279), (1,2203), (1,2281), (1,3217), ...}. - Hugo Pfoertner, Jan 12 2020

MATHEMATICA

Union@ Flatten@ Table[Select[Map[(1 + #)^n + (-#)^n &, Divisors@ n], PrimeQ], {n, 150}] (* Michael De Vlieger, Apr 29 2017 *)

CROSSREFS

Cf. A000668 (Mersenne primes), A019434 (Fermat primes), A243100, A285887, A285888.

Sequence in context: A314324 A247011 A172480 * A106069 A339691 A076294

Adjacent sequences:  A285883 A285884 A285885 * A285887 A285888 A285889

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Apr 27 2017

EXTENSIONS

Edited by N. J. A. Sloane, Jan 11 2020

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 29 07:48 EST 2021. Contains 349416 sequences. (Running on oeis4.)