A285111 - OEIS

A285111

Permutation of nonnegative integers: a(1) = 0, a(2) = 1, a(A005117(1+n)) = 2*a(n), a(A065642(n)) = 1 + 2*a(n).

0, 1, 2, 3, 4, 6, 8, 7, 5, 12, 16, 13, 14, 10, 24, 15, 32, 27, 26, 25, 28, 20, 48, 55, 9, 30, 11, 21, 64, 54, 52, 31, 50, 56, 40, 111, 96, 110, 18, 51, 60, 22, 42, 41, 49, 128, 108, 223, 17, 103, 104, 61, 62, 447, 100, 43, 112, 80, 222, 109, 192, 220, 57, 63, 36, 102, 120, 113, 44, 84, 82, 895, 98, 256, 99, 221, 216, 446, 34, 207, 23

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

Note the indexing: the domain starts from 1, while the range includes also zero.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(1) = 0, a(2) = 1, and for n > 2, if A008683(n) <> 0 [when n is squarefree], a(n) = 2*a(A013928(n)), otherwise a(n) = 1 + 2*a(A285328(n)).

PROG

(Scheme, with memoization-macro definec)

(definec (A285111 n) (cond ((<= n 2) (- n 1)) ((not (zero? (A008683 n))) (* 2 (A285111 (A013928 n)))) (else (+ 1 (* 2 (A285111 (A285328 n)))))))

(Python)

from operator import mul

from sympy import primefactors

from sympy.ntheory.factor_ import core

from functools import reduce

def a007947(n): return 1 if n<2 else reduce(mul, primefactors(n))

def a285328(n):

if core(n) == n: return 1

k=n - 1

while k>0:

if a007947(k) == a007947(n): return k

else: k-=1

def a013928(n): return sum([1 for i in range(1, n) if core(i) == i])

def a(n):

if n<3: return n - 1

if core(n)==n: return 2*a(a013928(n))

else: return 1 + 2*a(a285328(n))

print([a(n) for n in range(1, 121)]) # Indranil Ghosh, Apr 17 2017

CROSSREFS

Inverse: A285112.

Cf. A005117, A008683, A013928, A065642, A285328.

Similar or related permutations: A243343, A243345, A277695, A284571.

Sequence in context: A082315 A342266 A082320 * A253566 A333220 A176798

Adjacent sequences: A285108 A285109 A285110 * A285112 A285113 A285114

KEYWORD

nonn

AUTHOR

Antti Karttunen, Apr 17 2017

STATUS

approved