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

Author

Juri-Stepan Gerasimov, Apr 27 2017

Keywords

• nonn

Comments

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

Examples

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

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.

Crossrefs

Cf. A285886, A285888.

Programs

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 *)

Extensions

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