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A079298 Binomial numbers: of the form a^k +- b^k for k >= 2.

%I A079298 #10 Feb 16 2025 08:32:48
%S A079298 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 A079298 29,31,32,33,34,35,36,37,39,40,41,43,44,45,47,48,49,50,51,52,53,54,55,
%U A079298 56,57,58,59,60,61,63,64,65,67,68,69,71,72,73,74,75,76,77,79,80,81,82
%N A079298 Binomial numbers: of the form a^k +- b^k for k >= 2.
%H A079298 Robert Israel, <a href="/A079298/b079298.txt">Table of n, a(n) for n = 1..10000</a>
%H A079298 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BinomialNumber.html">Binomial Number.</a>
%e A079298 10 = 3^2+1^2; 13 = 7^2-6^2; 54 = 3^3+3^3.
%p A079298 N:= 200: # for all terms <= N
%p A079298 kmax:= floor(LambertW(2*ln(2)*N)/ln(2)):
%p A079298 S:= {0};
%p A079298 for k from 2 to kmax do
%p A079298   bmax:= floor((N/k)^(1/(k-1)));
%p A079298   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 A079298 od:
%p A079298 sort(convert(S,list)); # _Robert Israel_, Jan 03 2019
%Y A079298 Complement of A079299.
%K A079298 nonn
%O A079298 1,3
%A A079298 _David W. Wilson_, Feb 09 2003