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A377933 First differences of consecutive perfect powers m^k with k>=3 (A076467).

%I A377933 #17 Nov 26 2024 12:02:17
%S A377933 7,8,11,5,32,17,44,3,88,27,13,87,169,113,104,271,24,272,35,397,320,
%T A377933 139,10,204,343,381,250,721,817,919,729,298,917,224,192,1069,739,648,
%U A377933 1519,1657,817,984,759,423,769,2107,1053,1216,2437,2611,1561,1230,2977,3169,2479,888
%N A377933 First differences of consecutive perfect powers m^k with k>=3 (A076467).
%H A377933 Hugo Pfoertner, <a href="/A377933/b377933.txt">Table of n, a(n) for n = 1..10000</a>
%H A377933 <a href="/plot2a?name1=A000027&amp;name2=A377933&amp;tform1=log+base+10&amp;tform2=log+base+10&amp;shift=0&amp;radiop1=xy&amp;drawpoints=true">Plot of log_10(a(n)) vs log_10(n)</a>, using Plot 2.
%F A377933 a(n) = A076467(n+1) - A076467(n).
%p A377933 N:= 10^5: # for terms <= N of A076467
%p A377933 S:= sort(convert({1, seq(seq(m^k, m = 2 .. floor(N^(1/k))), k=3..ilog2(N))},list)):
%p A377933 S[2..-1]-S[1..-2]; # _Robert Israel_, Nov 24 2024
%o A377933 (PARI) lista(nn) = my(S=List(1)); for(x=2, sqrtnint(nn, 3), for(k=3, logint(nn, x), listput(S, x^k))); my(v=Set(S)); vector(#v-1, k, v[k+1]-v[k]); \\ _Michel Marcus_, Nov 24 2024
%Y A377933 Cf. A001597, A053289, A076467.
%K A377933 nonn,easy
%O A377933 1,1
%A A377933 _Hugo Pfoertner_, Nov 24 2024