A324116 - OEIS

%I #9 Feb 20 2019 21:43:08

%S 1,1,1,3,1,4,1,2,5,5,1,3,1,6,7,8,1,2,1,4,9,7,1,13,7,8,5,5,1,3,1,7,11,

%T 9,10,12,1,10,13,18,1,4,1,6,8,11,1,12,9,2,15,7,1,11,13,23,17,12,1,19,

%U 1,13,11,13,16,5,1,8,19,3,1,13,1,14,7,9,13,6,1,17,10,15,1,26,19,16,21,28,1,18,17,10,23,17,22,23,1,2

%N a(n) = A002487(1+A323247(n)) = A324288(A156552(n)).

%C Like A323902, this also has quite a moderate growth rate, even though a certain subset of terms of A156552 soon grow quite big.

%H Antti Karttunen, <a href="/A324116/b324116.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A324116/a324116.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>

%F a(n) = A002487(1+A323247(n)) = A324288(A156552(n)).

%F a(p) = 1 for all primes p.

%o (PARI)

%o A002487(n) = { my(s=sign(n), a=1, b=0); n = abs(n); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (s*b); }; \\ So we use this one, modified from the one given in A002487

%o A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };

%o 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 A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));

%o A324288(n) = A002487(1+A005187(n));

%o A324116(n) = A324288(A156552(n));

%Y Cf. A002487, A005187, A156552, A323247, A323902, A324115, A324288.

%K nonn

%O 1,4

%A _Antti Karttunen_, Feb 20 2019