A277195 Permutation of nonnegative integers: a(n) = A022290(A277010(n)).

0, 1, 2, 3, 4, 5, 6, 8, 13, 9, 7, 21, 34, 10, 14, 55, 22, 89, 12, 144, 15, 35, 11, 233, 56, 23, 377, 17, 610, 90, 987, 36, 1597, 16, 57, 145, 2584, 4181, 234, 24, 25, 6765, 91, 19, 10946, 17711, 378, 18, 38, 28657, 611, 46368, 37, 988, 146, 75025, 26, 235, 1598, 58, 121393, 196418, 59, 317811, 20, 2585, 514229, 832040, 27, 379, 1346269, 93, 92

Offset: 1

Author

Antti Karttunen, Oct 07 2016

Keywords

• nonn

Comments

Note the indexing: domain starts from 1, but the range includes also 0.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1024
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A277196.

Cf. A005117, A022290, A156552, A277010.

Programs

Python

from math import isqrt
from sympy import fibonacci, mobius, primepi, factorint
def A277195(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(fibonacci(primepi(p)+i) for i, p in enumerate(factorint(bisection(f), multiple=True),1)) # Chai Wah Wu, Aug 31 2024

Scheme

(define (A277195 n) (A022290 (A277010 n)))

Formula

a(n) = A022290(A277010(n)) = A022290(A156552(A005117(n))).