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A323902 a(n) = A002487(A156552(n)).

%I A323902 #11 Feb 10 2019 23:06:24
%S A323902 0,1,1,2,1,3,1,3,2,4,1,5,1,5,3,4,1,5,1,7,4,6,1,7,2,7,3,9,1,8,1,5,5,8,
%T A323902 3,8,1,9,6,10,1,11,1,11,5,10,1,9,2,7,7,13,1,7,4,13,8,11,1,13,1,12,7,6,
%U A323902 5,14,1,15,9,11,1,11,1,13,5,17,3,17,1,13,4,14,1,18,6,15,10,16,1,12,4,19,11,16,7,11,1,9,9,12,1,20,1,19,8
%N A323902 a(n) = A002487(A156552(n)).
%C A323902 Even though certain subset of terms of A156552 soon grow quite big, this sequence still has a quite moderate growth rate, thanks to the compensating effect of A002487.
%H A323902 Antti Karttunen, <a href="/A323902/b323902.txt">Table of n, a(n) for n = 1..16384</a>
%H A323902 Antti Karttunen, <a href="/A323902/a323902.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A323902 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A323902 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A323902 <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%F A323902 a(n) = A002487(A156552(n)) = A002487(A322993(n)).
%F A323902 a(p) = 1 for all primes p.
%o A323902 (PARI)
%o A323902 A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487
%o A323902 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A323902 A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
%o A323902 A323902(n) = A002487(A156552(n));
%Y A323902 Cf. A002487, A156552, A322993.
%Y A323902 Cf. also A323240, A323244, A323901, A323903.
%K A323902 nonn
%O A323902 1,4
%A A323902 _Antti Karttunen_, Feb 09 2019