A285887 Primes of the form (1 + x)^y + (-x)^y where y is a divisor of x.

13, 37, 41, 127, 271, 313, 421, 881, 1013, 1201, 1801, 1861, 2113, 2269, 2381, 2791, 3613, 4651, 5101, 5419, 6211, 7057, 7321, 9941, 10513, 10657, 12097, 13267, 13613, 14281, 16381, 19927, 20201, 21013, 21841, 24421, 24571, 26227, 30013, 33391, 34061, 35317, 41761, 45757, 47741, 49297

Offset

1,1

Comments

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

Links

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

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

Example

13 is in this sequence because (1 + 2)^2 + (-2)^2 = 13 is prime where 2 is divisor of 2.

Maple

N:= 100000: # To get terms <= N
Res:= NULL:
for y from 2 while 2^y -1 <= N do
z:= y/2^padic:-ordp(y, 2);
if z > 1 and (z <> y or not isprime(z)) then next fi;
for x from y by y do
  v:= (1+x)^y + (-x)^y;
  if v > N then break fi;
  if isprime(v) then Res:= Res, v; fi
od od:
sort(convert({Res}, list)); # Robert Israel, Jan 05 2020

Mathematica

Union@ Flatten@ Table[Select[Map[(1 + n)^# + (-n)^# &, Divisors@ n], PrimeQ], {n, 200}] (* Michael De Vlieger, Apr 29 2017 *)

Crossrefs

Cf. A285886, A285888.

Sequence in context: A220462 A280997 A185006 * A063913 A119705 A343895

Adjacent sequences: A285884 A285885 A285886 * A285888 A285889 A285890

Keyword

nonn

Author

Juri-Stepan Gerasimov, Apr 27 2017

Extensions

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

Status

approved