A285886 Primes of the form (1 + x)^y + (-x)^y where x is a divisor of y.

5, 7, 13, 17, 31, 37, 97, 127, 257, 881, 4651, 8191, 65537, 131071, 524287, 1273609, 2147483647, 2305843009213693951, 618970019642690137449562111, 3512911982806776822251393039617, 162259276829213363391578010288127, 170141183460469231731687303715884105727

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