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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 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

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