cp's OEIS Frontend

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

%I A285887 #28 Dec 23 2024 14:53:45
%S A285887 13,37,41,127,271,313,421,881,1013,1201,1801,1861,2113,2269,2381,2791,
%T A285887 3613,4651,5101,5419,6211,7057,7321,9941,10513,10657,12097,13267,
%U A285887 13613,14281,16381,19927,20201,21013,21841,24421,24571,26227,30013,33391,34061,35317,41761,45757,47741,49297
%N A285887 Primes of the form (1 + x)^y + (-x)^y where y is a divisor of x.
%C A285887 If x = y then: 13, 37, 881, 4651, 1273609, ...
%H A285887 Robert Israel, <a href="/A285887/b285887.txt">Table of n, a(n) for n = 1..10000</a>
%H A285887 J. S. Gerasimov, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2014-August/013480.html">x^(y + 1) - y^x</a>, SeqFan list, Aug 18 2014.
%e A285887 13 is in this sequence because (1 + 2)^2 + (-2)^2 = 13 is prime where 2 is divisor of 2.
%p A285887 N:= 100000: # To get terms <= N
%p A285887 Res:= NULL:
%p A285887 for y from 2 while 2^y -1 <= N do
%p A285887 z:= y/2^padic:-ordp(y, 2);
%p A285887 if z > 1 and (z <> y or not isprime(z)) then next fi;
%p A285887 for x from y by y do
%p A285887   v:= (1+x)^y + (-x)^y;
%p A285887   if v > N then break fi;
%p A285887   if isprime(v) then Res:= Res, v; fi
%p A285887 od od:
%p A285887 sort(convert({Res}, list)); # _Robert Israel_, Jan 05 2020
%t A285887 Union@ Flatten@ Table[Select[Map[(1 + n)^# + (-n)^# &, Divisors@ n], PrimeQ], {n, 200}] (* _Michael De Vlieger_, Apr 29 2017 *)
%Y A285887 Cf. A285886, A285888.
%K A285887 nonn
%O A285887 1,1
%A A285887 _Juri-Stepan Gerasimov_, Apr 27 2017
%E A285887 Edited by _N. J. A. Sloane_, Jan 11 2020