
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, 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, 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
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OFFSET

1,4


COMMENTS

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.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Index entries for sequences related to binary expansion of n
Index entries for sequences computed from indices in prime factorization
Index entries for sequences related to Stern's sequences


FORMULA

a(n) = A002487(A156552(n)) = A002487(A322993(n)).
a(p) = 1 for all primes p.


PROG

(PARI)
A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487
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)};
A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
A323902(n) = A002487(A156552(n));


CROSSREFS

Cf. A002487, A156552, A322993.
Cf. also A323240, A323244, A323901, A323903.
Sequence in context: A020650 A124224 A290089 * A331991 A309634 A309633
Adjacent sequences: A323899 A323900 A323901 * A323903 A323904 A323905


KEYWORD

nonn


AUTHOR

Antti Karttunen, Feb 09 2019


STATUS

approved

