A088905 Numbers m having exactly one representation m = x^i + x^j with 1

2, 3, 7, 11, 13, 15, 19, 21, 23, 25, 27, 29, 31, 35, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 131, 133, 135, 137, 139, 141

Offset: 1

Author

Reinhard Zumkeller, Oct 21 2003

Keywords

• nonn

Comments

A088904(a(n)) = 1.

All terms > 2 are odd. - Robert Israel, Dec 05 2019

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Programs

Maple

filter:= proc(n) local F, t,d,s,r,b;
   F:= ifactors(n-1)[2];
   d:= igcd(seq(t[2],t=F));
   if d > 1 then return false fi;
   for s in numtheory:-divisors(n) minus {1,n} do
     r:= n/s-1;
     F:= ifactors(s)[2];
     d:= igcd(seq(t[2],t=F));
     b:= mul(t[1]^(t[2]/d),t=F);
     if r = b^padic:-ordp(r,b) then return false fi
   od;
   true
end proc:
select(filter, [2,seq(i,i=3..1000,2)]); # Robert Israel, Dec 05 2019

Mathematica

M = 200;
V = 2 - Mod[Range[M], 2];
For[x = 2, 1 + x^2 <= M, x++, For[i = 0, 2 x^i <= M, i++, For[j = Max[2, i], True, j++, t = x^i + x^j; If[t > M, Break[]]; V[[t]]++]]];
V[[1]] = 0; V[[2]] = 1;
Position[V, 1] // Flatten (* Jean-François Alcover, Jun 17 2020, after Robert Israel in A088904 *)

Extensions

Entry completely revised: Hugo Pfoertner and Reinhard Zumkeller, Oct 20 2004