This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
lst={};k=7;Do[If[PrimeQ[Abs[k^n-n^k]], AppendTo[lst, n]], {n, 0, 10^4}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 10 2008 *)
is(n)=isprime(abs(7^n-n^7)) \\ Charles R Greathouse IV, Feb 17 2017
lst={};k=8;Do[If[PrimeQ[Abs[k^n-n^k]], AppendTo[lst, n]], {n, 0, 10^4}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 10 2008 *)
is(n)=isprime(8^n-n^8) \\ Charles R Greathouse IV, Feb 17 2017
lst={};k=9;Do[If[PrimeQ[Abs[k^n-n^k]], AppendTo[lst, n]], {n, 0, 10^4}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 10 2008 *)
is(n)=isprime(abs(9^n-n^9)) \\ Charles R Greathouse IV, Feb 17 2017
[n: n in [0..500]| IsPrime(10^n-n^10)]; // Vincenzo Librandi, Apr 01 2015
lst={};k=10;Do[If[PrimeQ[Abs[k^n-n^k]], AppendTo[lst, n]], {n, 0, 10^4}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 10 2008 *)
Select[Range[0, 10000], PrimeQ[10^# - #^10] &] (* Vincenzo Librandi, Apr 01 2015 *)
is(n)=isprime(abs(10^n-n^10)) \\ Charles R Greathouse IV, Feb 17 2017
lst={};k=11;Do[If[PrimeQ[Abs[k^n-n^k]], AppendTo[lst, n]], {n, 0, 10^4}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 10 2008 *)
is(n)=ispseudoprime(abs(11^n-n^11)) \\ Charles R Greathouse IV, Feb 17 2017
The primes 6102977801 and 1490116119372884249 are of the form 5^y-y^5 (for y=14 and y=26) and therefore members of this sequence. The next larger primes of this form would have y > 4500 and would be much too large to be included. - _M. F. Hasler_, Aug 19 2014
N:= 10^100: # to get all terms <= N
A:= NULL:
for x from 2 while x^(x+1) - (x+1)^x <= N do
for y from x+1 do
z:= x^y - y^x;
if z > N then break
elif z > 0 and isprime(z) then A:=A, z;
fi
od od:
{A}; # Robert Israel, Aug 29 2014
Take[Select[Intersection[Flatten[Table[Abs[x^y-y^x],{x,2,120},{y,2,120}]]],PrimeQ[ # ]&],25]
nn=10^50; n=1; t=Union[Reap[While[n++; k=n+1; num=Abs[n^k-k^n]; num0&&PrimeQ[#]&]],nn]] (* Harvey P. Dale, Nov 23 2013 *)
a=[];for(S=1,199,for(x=2,S-2,ispseudoprime(p=x^(y=S-x)-y^x)&&a=concat(a,p)));Set(a) \\ May be incomplete in the upper range of values, i.e., beyond a given S=x+y, a larger S may yield a smaller prime (for small x). - M. F. Hasler, Aug 19 2014
Do[If[PrimeQ[Abs[14^n - n^14]], Print[n]], {n, 10^4}] (* Ryan Propper, Mar 27 2007 *)
is(n)=ispseudoprime(abs(14^n-n^14)) \\ Charles R Greathouse IV, Feb 17 2017
a(1) = 1 because (1^k - k^1) = (1 - k) < 0 for k > 1. a(2) = 7 because 2^5 - 5^2 = 7 is prime, but (2^k - k^2) is not prime for 1 < k < 5, (2^2 - 2^2) = 0, (2^3 - 3^2) = -1, (2^4 - 4^2) = 0. a(4) = 1 because no prime of the form (4^k - k^4) exists; 4^k - k^4 = (2^k - k^2)*(2^k + k^2). a(12) = 83695120256591 = 12^13 - 13^12 = A024152(A122003(2)).
Select[Table[6^x-x^6,{x,200}],PrimeQ] (* Harvey P. Dale, Jan 17 2018 *)
for(x=1,1e5,ispseudoprime(p=6^x-x^6)&&print1(p","))
Comments