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A287051 a(0) = 0, a(1) = 1; a(2*n) = gpf(a(n)), a(2*n+1) = a(n) + a(n+1), where gpf(a(n)) is the greatest prime dividing a(n) for a(n) >= 2 and 1 if a(n) = 1 (A006530).

%I A287051 #7 Feb 16 2025 08:33:46
%S A287051 0,1,1,2,1,3,2,3,1,4,3,5,2,5,3,4,1,5,2,7,3,8,5,7,2,7,5,8,3,7,2,5,1,6,
%T A287051 5,7,2,9,7,10,3,11,2,13,5,12,7,9,2,9,7,12,5,13,2,11,3,10,7,9,2,7,5,6,
%U A287051 1,7,3,11,5,12,7,9,2,11,3,16,7,17,5,13,3,14,11,13,2,15,13,18,5,17,3,19,7,16,3,11,2,11,3,16,7
%N A287051 a(0) = 0, a(1) = 1; a(2*n) = gpf(a(n)), a(2*n+1) = a(n) + a(n+1), where gpf(a(n)) is the greatest prime dividing a(n) for a(n) >= 2 and 1 if a(n) = 1 (A006530).
%C A287051 A variation on Stern's diatomic sequence.
%H A287051 Michael Gilleland, <a href="/selfsimilar.html">Some Self-Similar Integer Sequences</a>
%H A287051 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GreatestPrimeFactor.html">Greatest Prime Factor</a>
%H A287051 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SternsDiatomicSeries.html">Stern's Diatomic Series</a>
%H A287051 <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%e A287051 a(0) = 0;
%e A287051 a(1) = 1;
%e A287051 a(2) = a(2*1) = gpf(a(1)) = 1;
%e A287051 a(3) = a(2*1+1) = a(1) + a(2) = 2;
%e A287051 a(4) = a(2*2) = gpf(a(2)) = 1;
%e A287051 a(5) = a(2*2+1) = a(2) + a(3) = 3;
%e A287051 a(6) = a(2*3) = gpf(a(3)) = 2, etc.
%t A287051 a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], FactorInteger[a[n/2]][[-1, 1]], a[(n - 1)/2] + a[(n + 1)/2]]; Table[a[n], {n, 0, 100}]
%Y A287051 Cf. A002487, A006530, A175723, A177904.
%K A287051 nonn
%O A287051 0,4
%A A287051 _Ilya Gutkovskiy_, May 18 2017