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A347296 a(1) = 1; for n >= 1, if a(n) is even then a(n+1) = a(n) / 2, otherwise, say a(n) is the k-th odd term in the sequence, a(n+1) = a(n) + a(k).

%I A347296 #12 Jan 25 2022 08:50:43
%S A347296 1,2,1,3,4,2,1,4,2,1,5,7,8,4,2,1,5,7,8,4,2,1,6,3,10,5,13,17,19,20,10,
%T A347296 5,10,5,12,6,3,11,15,17,18,9,15,18,9,19,24,12,6,3,16,8,4,2,1,18,9,28,
%U A347296 14,7,27,37,42,21,31,36,18,9,21,27,30,15,26,13,28
%N A347296 a(1) = 1; for n >= 1, if a(n) is even then a(n+1) = a(n) / 2, otherwise, say a(n) is the k-th odd term in the sequence, a(n+1) = a(n) + a(k).
%C A347296 This sequence is a variant of A350877; here we add terms of the sequence, there prime numbers.
%H A347296 Rémy Sigrist, <a href="/A347296/b347296.txt">Table of n, a(n) for n = 1..10000</a>
%e A347296 a(1) = 1.
%e A347296 a(2) = a(1) + a(1) = 2 as a(1) is the 1st odd term.
%e A347296 a(3) = a(2) / 2 = 1 as a(2) is even.
%e A347296 a(4) = a(3) + a(2) = 3 as a(3) is the 2nd odd term.
%e A347296 a(5) = a(4) + a(3) = 4 as a(4) is the 3rd odd term.
%o A347296 (PARI) k=0; for (n=1, #a=vector(75), print1 (a[n]=if (n==1, 1, a[n-1]%2==0, a[n-1]/2, a[n-1]+a[k++])", "))
%Y A347296 Cf. A347297, A350877.
%K A347296 nonn
%O A347296 1,2
%A A347296 _Rémy Sigrist_, Jan 23 2022