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Binomial numbers: of the form a^k +- b^k for k >= 2.
3

%I #9 Jan 03 2019 13:29:21

%S 0,1,2,3,4,5,7,8,9,10,11,12,13,15,16,17,18,19,20,21,23,24,25,26,27,28,

%T 29,31,32,33,34,35,36,37,39,40,41,43,44,45,47,48,49,50,51,52,53,54,55,

%U 56,57,58,59,60,61,63,64,65,67,68,69,71,72,73,74,75,76,77,79,80,81,82

%N Binomial numbers: of the form a^k +- b^k for k >= 2.

%H Robert Israel, <a href="/A079298/b079298.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BinomialNumber.html">Binomial Number.</a>

%e 10 = 3^2+1^2; 13 = 7^2-6^2; 54 = 3^3+3^3.

%p N:= 200: # for all terms <= N

%p kmax:= floor(LambertW(2*ln(2)*N)/ln(2)):

%p S:= {0};

%p for k from 2 to kmax do

%p bmax:= floor((N/k)^(1/(k-1)));

%p S:= S union select(`<=`,{seq(seq(b^k-a^k,a=0..b-1),b=1..bmax), seq(seq(b^k+a^k,a=0..b),b=1..floor(N^(1/k)))},N);

%p od:

%p sort(convert(S,list)); # _Robert Israel_, Jan 03 2019

%Y Complement of A079299.

%K nonn

%O 1,3

%A _David W. Wilson_, Feb 09 2003