A253893 -id:A253893 - cp's OEIS frontend

A253887 Row index of n in A191450: a(3n) = 2n, a(3n+1) = 2n+1, a(3n+2) = a(n+1).

1, 1, 2, 3, 1, 4, 5, 2, 6, 7, 3, 8, 9, 1, 10, 11, 4, 12, 13, 5, 14, 15, 2, 16, 17, 6, 18, 19, 7, 20, 21, 3, 22, 23, 8, 24, 25, 9, 26, 27, 1, 28, 29, 10, 30, 31, 11, 32, 33, 4, 34, 35, 12, 36, 37, 13, 38, 39, 5, 40, 41, 14, 42, 43, 15, 44, 45, 2, 46, 47, 16, 48, 49, 17, 50, 51, 6, 52, 53, 18, 54, 55, 19, 56, 57, 7

Offset: 1

Antti Karttunen, Jan 22 2015

nonn

a(n) gives the row index of n in square array A191450, or equally, the column index of n in A254051.

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

Odd bisection of A126760.
Cf. A254046 (the corresponding column index).
Cf. A003602, A032766, A064216, A253786, A253893, A249746.
Cf. A191450, A254051, A254047, A254052, A254104.

def a(n):
    if n%3==0: return 2*n//3
    elif n%3==1: return 2*(n - 1)//3 + 1
    else: return a((n - 2)//3 + 1)
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Jun 06 2017

a(3n) = 2n, a(3n+1) = 2n+1, a(3n+2) = a(n+1).
a(n) = A126760(2n-1).
a(n) = A249746(A003602(A064216(n))). - Antti Karttunen, Feb 04 2015

A253889 a(n) = A048673(floor(A064216(n)/2)).

Original entry on oeis.org

1, 1, 1, 2, 2, 3, 4, 3, 8, 14, 4, 13, 5, 5, 7, 17, 6, 6, 18, 7, 38, 32, 8, 28, 23, 9, 15, 11, 10, 26, 16, 11, 41, 53, 12, 33, 39, 13, 10, 113, 14, 43, 12, 15, 22, 63, 16, 25, 59, 17, 203, 74, 18, 48, 30, 19, 188, 50, 20, 122, 68, 21, 9, 149, 22, 138, 83, 23, 60, 86, 24, 35, 29, 25, 73, 62, 26, 24, 123, 27, 27, 128, 28, 313

Offset: 1

Antti Karttunen, Jan 22 2015

nonn

When A048673 is represented as a binary tree, then any non-root node k (>= 2) which contains value n = A048673(k) has as its parent a(n) = A048673(floor(k/2)).

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

Cf. A048673, A064216, A253888, A253893.

f[n_] := Times @@ Power[If[# == 1, 1, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger[2 n - 1]; g[n_] := (Times @@ Power[If[# == 1, 1, NextPrime@ #] & /@ First@ #, Last@ #] + 1)/2 &@ Transpose@ FactorInteger@ n; Array[Floor@ g[Floor[f[#]/2]] &, 84] (* Michael De Vlieger, Sep 16 2017 *)

(define (A253889 n) (A048673 (floor->exact (/ (A064216 n) 2))))

a(n) = A048673(floor(A064216(n)/2)).
Other identities. For all n >= 0:
a(3n+2) = n+1.

A253894 a(1) = 1, for n > 1, a(n) = 1 + a(A253889(n)).

Original entry on oeis.org

1, 2, 2, 3, 3, 3, 4, 3, 4, 5, 4, 5, 4, 4, 5, 5, 4, 4, 5, 5, 6, 6, 4, 6, 5, 5, 6, 5, 6, 6, 6, 5, 6, 6, 6, 7, 7, 5, 6, 7, 5, 7, 6, 6, 7, 6, 6, 6, 7, 5, 7, 7, 5, 7, 7, 6, 7, 6, 6, 7, 6, 7, 5, 7, 7, 7, 7, 5, 8, 8, 7, 7, 7, 6, 8, 8, 6, 7, 8, 7, 7, 8, 6, 8, 7, 7, 8, 6, 7, 8, 8, 7, 7, 7, 6, 8, 8, 7, 8, 8, 7, 7, 7, 7, 7, 8, 8, 7, 8, 8, 8, 8, 6, 8, 8, 7, 8, 8, 8, 8

Offset: 1

Antti Karttunen, Jan 22 2015

nonn

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

One more than A253893.
Sum of A254044 and A254045.
Cf. A064216, A070939, A253889.

a(1) = 1, for n > 1, a(n) = 1 + a(A253889(n)).
a(n) = A070939(A064216(n)). [Binary width of terms of A064216.]
a(n) = A253893(n) + 1.
a(n) = A254044(n) + A254045(n).

cp's OEIS Frontend

A253887 Row index of n in A191450: a(3n) = 2n, a(3n+1) = 2n+1, a(3n+2) = a(n+1).

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A253889 a(n) = A048673(floor(A064216(n)/2)).

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A253894 a(1) = 1, for n > 1, a(n) = 1 + a(A253889(n)).

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