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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
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane, Jan 11 2020
STATUS
approved

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Last modified May 29 14:43 EDT 2024. Contains 372952 sequences. (Running on oeis4.)