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

1,3

Comments

Permutation of A003714 (Fibbinary numbers).

Links

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

Formula

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

Other identities. For all n >= 1:

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

Prog

(Scheme) (define (A277010 n) (A156552 (A005117 n)))
(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<<primepi(p)+i for i, p in enumerate(factorint(bisection(f), multiple=True), -1)) # Chai Wah Wu, Aug 31 2024

Crossrefs

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

Cf. also A277006, A277020, A277195.

Sequence in context: A333256 A227369 A092739 * A101394 A095031 A100598

Adjacent sequences: A277007 A277008 A277009 * A277011 A277012 A277013

Keyword

nonn

Author

Antti Karttunen, Oct 07 2016

Status

approved