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Permutation of nonnegative integers: a(n) = A022290(A277010(n)).
4

%I #10 Aug 31 2024 14:45:53

%S 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,

%T 23,377,17,610,90,987,36,1597,16,57,145,2584,4181,234,24,25,6765,91,

%U 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

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

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

%H Antti Karttunen, <a href="/A277195/b277195.txt">Table of n, a(n) for n = 1..1024</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

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

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

%o (Python)

%o from math import isqrt

%o from sympy import fibonacci, mobius, primepi, factorint

%o def A277195(n):

%o def f(x): return n+x-sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))

%o def bisection(f,kmin=0,kmax=1):

%o while f(kmax) > kmax: kmax <<= 1

%o while kmax-kmin > 1:

%o kmid = kmax+kmin>>1

%o if f(kmid) <= kmid:

%o kmax = kmid

%o else:

%o kmin = kmid

%o return kmax

%o return sum(fibonacci(primepi(p)+i) for i, p in enumerate(factorint(bisection(f), multiple=True),1)) # _Chai Wah Wu_, Aug 31 2024

%Y Inverse: A277196.

%Y Cf. A005117, A022290, A156552, A277010.

%K nonn

%O 1,3

%A _Antti Karttunen_, Oct 07 2016