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A252463 Hybrid shift: a(1) = 1, a(2n) = n, a(2n+1) = A064989(2n+1); shift the even numbers one bit right, shift the prime factorization of odd numbers one step towards smaller primes. 51
1, 1, 2, 2, 3, 3, 5, 4, 4, 5, 7, 6, 11, 7, 6, 8, 13, 9, 17, 10, 10, 11, 19, 12, 9, 13, 8, 14, 23, 15, 29, 16, 14, 17, 15, 18, 31, 19, 22, 20, 37, 21, 41, 22, 12, 23, 43, 24, 25, 25, 26, 26, 47, 27, 21, 28, 34, 29, 53, 30, 59, 31, 20, 32, 33, 33, 61, 34, 38, 35, 67, 36, 71, 37, 18, 38, 35, 39, 73, 40, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

For any node n >= 2 in binary trees A005940 and A163511, a(n) gives the parent node of n. (Here we assume that their initial root 1 is its own parent).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..8192

FORMULA

a(1) = 1, a(2n) = n, a(2n+1) = A064989(2n+1).

Other identities. For all n >= 1:

a(2n-1) = A064216(n).

A001222(a(n)) = A001222(n) - (1 - A000035(n)).

Above means: if n is odd, A001222(a(n)) = A001222(n) and if n is even, A001222(a(n)) = A001222(n) - 1.

MATHEMATICA

Table[Which[n == 1, 1, EvenQ@ n, n/2, True, Times @@ Power[

Which[# == 1, 1, # == 2, 1, True, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger@ n], {n, 81}] (* Michael De Vlieger, Sep 16 2017 *)

PROG

(Scheme) (define (A252463 n) (cond ((<= n 1) n) ((even? n) (/ n 2)) (else (A064989 n))))

(Python)

from sympy import factorint, prevprime

from operator import mul

def a064989(n):

    f=factorint(n)

    return 1 if n==1 else reduce(mul, [1 if i==2 else prevprime(i)**f[i] for i in f])

def a(n): return 1 if n==1 else n/2 if n%2==0 else a064989(n)

print(map(a, range(1, 101))) # Indranil Ghosh, Sep 15 2017

CROSSREFS

A252464 gives the number of iterations needed to reach 1 from n.

Bisections: A000027 and A064216.

Cf. A000035, A001222, A004526, A005940, A163511, A064989, A246277, A252461, A252462.

Sequence in context: A039649 A214288 A253554 * A113605 A307815 A070230

Adjacent sequences:  A252460 A252461 A252462 * A252464 A252465 A252466

KEYWORD

nonn

AUTHOR

Antti Karttunen, Dec 20 2014

STATUS

approved

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Last modified October 15 10:15 EDT 2019. Contains 328026 sequences. (Running on oeis4.)