A285887 - OEIS

%I #28 Dec 23 2024 14:53:45

%S 13,37,41,127,271,313,421,881,1013,1201,1801,1861,2113,2269,2381,2791,

%T 3613,4651,5101,5419,6211,7057,7321,9941,10513,10657,12097,13267,

%U 13613,14281,16381,19927,20201,21013,21841,24421,24571,26227,30013,33391,34061,35317,41761,45757,47741,49297

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

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

%H Robert Israel, <a href="/A285887/b285887.txt">Table of n, a(n) for n = 1..10000</a>

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

%p N:= 100000: # To get terms <= N

%p Res:= NULL:

%p for y from 2 while 2^y -1 <= N do

%p z:= y/2^padic:-ordp(y, 2);

%p if z > 1 and (z <> y or not isprime(z)) then next fi;

%p for x from y by y do

%p   v:= (1+x)^y + (-x)^y;

%p   if v > N then break fi;

%p   if isprime(v) then Res:= Res, v; fi

%p od od:

%p sort(convert({Res}, list)); # _Robert Israel_, Jan 05 2020

%t Union@ Flatten@ Table[Select[Map[(1 + n)^# + (-n)^# &, Divisors@ n], PrimeQ], {n, 200}] (* _Michael De Vlieger_, Apr 29 2017 *)

%Y Cf. A285886, A285888.

%K nonn,changed

%O 1,1

%A _Juri-Stepan Gerasimov_, Apr 27 2017

%E Edited by _N. J. A. Sloane_, Jan 11 2020