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A213714 Inverse function for injection A005187. 24
0, 1, 0, 2, 3, 0, 0, 4, 5, 0, 6, 7, 0, 0, 0, 8, 9, 0, 10, 11, 0, 0, 12, 13, 0, 14, 15, 0, 0, 0, 0, 16, 17, 0, 18, 19, 0, 0, 20, 21, 0, 22, 23, 0, 0, 0, 24, 25, 0, 26, 27, 0, 0, 28, 29, 0, 30, 31, 0, 0, 0, 0, 0, 32, 33, 0, 34, 35, 0, 0, 36, 37, 0, 38, 39, 0, 0, 0, 40, 41, 0, 42, 43, 0, 0, 44, 45, 0, 46, 47, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(0)=0; thereafter if n occurs as a term of A005187, a(n)=its position in A005187, otherwise zero. This works as an "inverse" function for A005187 in a sense that a(A005187(n)) = n for all n.

a(n)*A234017(n) = 0 for all n.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..8192

FORMULA

a(0)=0, for n>0, a(n) = A079559(n) * (A046699(n+2)-1) [With A046699's October 2012 starting offset. Incorrect indexing shown in this formula corrected by Antti Karttunen, Dec 18 2013]

PROG

(MIT/GNU Scheme)

(define (A213714 n) (if (< n 1) 0 (* (A079559 n) (- (A046699 (+ n 2)) 1)))) ;; With A046699's October 2012 starting offset.

(Haskell)

import Data.List (genericIndex)

a213714 n = genericIndex a213714_list n

a213714_list = f [0..] a005187_list 0 where

   f (x:xs) ys'@(y:ys) i | x == y    = i : f xs ys (i+1)

                         | otherwise = 0 : f xs ys' i

-- Reinhard Zumkeller, May 01 2015

(Python)

from sympy import factorial

def a046699(n):

    if n<3: return 1

    s=1

    while factorial(2*s)%(2**(n - 1))>0: s+=1

    return s

def a053644(n): return 0 if n==0 else 2**(len(bin(n)[2:]) - 1)

def a043545(n):

    x=bin(n)[2:]

    return int(max(x)) - int(min(x))

def a079559(n): return 1 if n==0 else a043545(n + 1)*a079559(n + 1 - a053644(n + 1))

def a(n): return 0 if n==0 else a079559(n)*(a046699(n + 2) - 1) # Indranil Ghosh, Jun 11 2017

CROSSREFS

Can be used when computing A213715, A213723, A213724, A233275, A233277. Cf. A005187, A046699, A079559, A234017, A230414.

Sequence in context: A072741 A131360 A338780 * A242011 A259657 A332672

Adjacent sequences:  A213711 A213712 A213713 * A213715 A213716 A213717

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 26 2012

STATUS

approved

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Last modified June 13 20:25 EDT 2021. Contains 345009 sequences. (Running on oeis4.)