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
KEYWORD
nonn
AUTHOR
Juri-Stepan Gerasimov, Apr 27 2017
EXTENSIONS
Edited by N. J. A. Sloane, Jan 11 2020
STATUS
approved