A277195 - OEIS

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A277195

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

4

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

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OFFSET

1,3

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

FORMULA

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

PROG

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

(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

CROSSREFS

Inverse: A277196.

Cf. A005117, A022290, A156552, A277010.

Sequence in context: A337448 A019532 A008537 * A358208 A133430 A033071

Adjacent sequences: A277192 A277193 A277194 * A277196 A277197 A277198

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 07 2016

STATUS

approved