A324287 a(n) = A002487(A005187(n)).

0, 1, 2, 1, 3, 1, 3, 5, 4, 1, 4, 7, 5, 7, 7, 5, 5, 1, 5, 9, 7, 10, 11, 8, 7, 9, 9, 7, 13, 8, 3, 10, 6, 1, 6, 11, 9, 13, 15, 11, 10, 13, 14, 11, 21, 13, 5, 17, 9, 11, 11, 9, 19, 12, 5, 18, 19, 11, 3, 13, 7, 18, 15, 4, 7, 1, 7, 13, 11, 16, 19, 14, 13, 17, 19, 15, 29, 18, 7, 24, 13, 16, 17, 14, 30, 19, 8, 29, 31, 18, 5, 22, 12, 31, 26, 7

Offset

0,3

Comments

The motivation for this kind of sequence was a question: what kind of simply defined non-injective functions f exist such that this sequence can be defined as their function, e.g., as a(n) = g(f(n)), where g is a nontrivial integer-valued function? The same question can also be asked about A324288, A324337 and A324338. Note that A005187, A283477 and A006068 used in their definitions are all injections. Of course, A324377(n) = A000265(A005187(n)) fills the bill as A002487(n) = A002487(A000265(n)), but are there any less obvious solutions? - Antti Karttunen, Feb 28 2019

Links

Antti Karttunen, Table of n, a(n) for n = 0..16385

Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537

Index entries for sequences related to binary expansion of n

Index entries for sequences related to Stern's sequences

Formula

a(n) = A002487(A005187(n)).

a(n) = A324286(A283477(n)).

a(n) = A002487(A324377(n)).

Prog

(PARI)
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); }; \\ Modified from the one given in A002487, sign not actually needed here.
A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
A324287(n) = A002487(A005187(n));
(Python)
from functools import reduce
def A324287(n): return sum(reduce(lambda x, y:(x[0], x[0]+x[1]) if int(y) else (x[0]+x[1], x[1]), bin((n<<1)-n.bit_count())[-1:2:-1], (1, 0))) if n else 0 # Chai Wah Wu, May 05 2023

Crossrefs

Cf. A000265, A002487, A005187, A006068, A283477, A324286, A324288, A324293, A324337, A324338, A324377.

Sequence in context: A380507 A321893 A308673 * A213594 A335105 A350597

Adjacent sequences: A324284 A324285 A324286 * A324288 A324289 A324290

Keyword

nonn

Author

Antti Karttunen, Feb 20 2019

Status

approved