A277010 a(n) = A156552(A005117(n)); permutation of Fibbinary numbers.

0, 1, 2, 4, 5, 8, 9, 16, 32, 17, 10, 64, 128, 18, 33, 256, 65, 512, 21, 1024, 34, 129, 20, 2048, 257, 66, 4096, 37, 8192, 513, 16384, 130, 32768, 36, 258, 1025, 65536, 131072, 2049, 68, 69, 262144, 514, 41, 524288, 1048576, 4097, 40, 133, 2097152, 8193, 4194304, 132, 16385, 1026, 8388608, 72, 2050, 32769, 260, 16777216, 33554432, 261, 67108864, 42

Offset: 1

Author

Antti Karttunen, Oct 07 2016

Keywords

• nonn

Comments

Permutation of A003714 (Fibbinary numbers).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1025

Crossrefs

Cf. A000040, A003714, A005117, A071403, A156552.

Cf. also A277006, A277020, A277195.

Programs

Python

from math import isqrt
from sympy import mobius, primepi, factorint
def A277010(n):
    def f(x): return n+x-sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))
    def bisection(f,kmin=0,kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    return sum(1<Chai Wah Wu, Aug 31 2024

Scheme

(define (A277010 n) (A156552 (A005117 n)))

Formula

a(n) = A156552(A005117(n)).

Other identities. For all n >= 1:

a(A071403(n)) = A000079(n-1).