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%I #13 Oct 10 2019 11:40:41
%S 0,1,3,5,4,12,13,14,2,6,10,15,17,8,19,30,34,47,53,11,16,9,7,18,31,33,
%T 48,52,29,20,44,37,27,22,42,39,25,24,40,41,23,26,38,43,21,28,36,45,55,
%U 66,59,62,63,58,67,54,46,35,65,56,69,75,50,71,57,64,61,60,68,32,49,51,70
%N a(0)=0; a(n) = smallest positive integer not occurring earlier in the sequence such that a(n-1)+a(n) = j^k, j = any positive integer, k = any integer >= 2.
%H Rémy Sigrist, <a href="/A127397/b127397.txt">Table of n, a(n) for n = 0..10000</a>
%t f[n_] := n == 1 || GCD @@ Last /@ FactorInteger[n] > 1;g[l_List] := Block[{k = 1},While[MemberQ[l, k] || ! f[k + l[[ -1]]], k++ ];Append[l, k]];Nest[g, {0}, 73] (* _Ray Chandler_, Jan 22 2007 *)
%Y Cf. A001597, A034175, A127398.
%K nonn,look
%O 0,3
%A _Leroy Quet_, Jan 12 2007
%E Extended by _Ray Chandler_, Jan 22 2007
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