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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.)