A303744 - OEIS

%I #24 Jun 25 2018 22:51:03

%S 1,2,4,6,10,14,18,22,30,34,38,42,46,50,54,58,62,66,70,74,78,82,86,90,

%T 94,102,106,110,114,118,122,126,130,134,138,142,146,150,154,158,162,

%U 166,170,174,178,182,186,190,194,198,202,206,210,214,222,226,230,234,238,246,250,254,258,262,266,270,274,278,282,286,290

%N Numbers that are not a difference between same powers (greater than 1) of positive numbers.

%C Apart from 1 and 4, all terms == 2 (mod 4). - _Robert Israel_, Jun 25 2018

%H Robert Israel, <a href="/A303744/b303744.txt">Table of n, a(n) for n = 1..10000</a>

%e Odd numbers greater than 1 are differences of squares, so they are not here.

%e 8 is not a term, 9 - 1: difference of two squares;

%e 26 is not a term, 27 - 1: difference of two cubes.

%p N:= 1000: # to get all terms <= N

%p S:= {1,2,4,seq(i,i=6..N,4)}:

%p for p from 3 to ilog2(N+1) do

%p   for n from 1 while n^p - (n-1)^p <= N do

%p     if n^p > N then m0:= ceil((n^p - N)^(1/p)) else m0:= 1 fi;

%p     for m from m0 to n-1 do

%p       v:= n^p-m^p;

%p       S:= S minus {v};

%p     od

%p od od:

%p sort(convert(S,list)); # _Robert Israel_, Jun 25 2018

%Y Sequences of numbers that are difference of powers: A024352 (squares), A181123 (cubes).

%Y And of further n-th powers: A147857 (4th), A181124 (5th), A181125 (6th), A181126 (7th), A181127 (8th), A181128 (9th).

%K nonn

%O 1,2

%A _Adam Kertesz_, Apr 29 2018