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A064273 Permutation of nonnegative integers: a(n) = A013928(A019565(n)). 3
0, 1, 2, 4, 3, 6, 10, 18, 5, 9, 13, 27, 22, 43, 64, 128, 7, 14, 20, 40, 33, 68, 100, 202, 47, 93, 143, 282, 232, 469, 702, 1404, 8, 16, 25, 48, 39, 79, 119, 235, 56, 110, 167, 333, 278, 553, 832, 1660, 88, 175, 260, 520, 437, 872, 1303, 2609, 608, 1216, 1826, 3649 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

From Antti Karttunen, Aug 24 2014: (Start)

The original name of the sequence was: "Inverse of sequence A048672 considered as a permutation of the nonnegative integers".

However, the real inverse to A048672 is A246353(n) (= a(n)+1), satisfying A246353(A048672(n)) = n for all n. This sequence subtracts one from the terms of A246353 so as to obtain a permutation of nonnegative integers (bijection [0..] --> [0..]).

Sequence is obtained when the range of A019565 is compacted so that it becomes surjective, thus the logarithmic scatter plots look very similar. (Same applies to A246353). Compare also to the plot of A005940.

(End)

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..478

Index entries for sequences that are permutations of the natural numbers

FORMULA

From Antti Karttunen, Aug 24 2014: (Start)

a(n) = A013928(A019565(n)).

a(n) = A246353(n) - 1.

(End)

PROG

(PARI)

allocatemem(234567890);

default(primelimit, 2^22)

uplim_for_13928 = 13123111;

v013928 = vector(uplim_for_13928); A013928(n) = v013928[n];

v013928[1]=0; n=1; while((n < uplim_for_13928), if(issquarefree(n), v013928[n+1] = v013928[n]+1, v013928[n+1] = v013928[n]); n++);

A019565(n) = {factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ This function from M. F. Hasler

A064273(n) = A013928(A019565(n));

for(n=0, 478, write("b064273.txt", n, " ", A064273(n))); \\ From Antti Karttunen, Aug 23 2014

(Scheme) (define (A064273 n) (let loop ((n n) (i 1) (p 1)) (cond ((zero? n) (- (A013928 (+ 1 p)) 1)) ((odd? n) (loop (/ (- n 1) 2) (+ 1 i) (* p (A000040 i)))) (else (loop (/ n 2) (+ 1 i) p))))) ;; Antti Karttunen, Aug 23 2014

CROSSREFS

One less than A246353.

Cf. A000040, A005940, A013928, A019565, A048672.

Sequence in context: A131393 A216476 A002326 * A232564 A134561 A225055

Adjacent sequences:  A064270 A064271 A064272 * A064274 A064275 A064276

KEYWORD

easy,nonn

AUTHOR

Howard A. Landman, Sep 23 2001

EXTENSIONS

More terms from Carl R. White, Apr 19 2006

Name changed by Antti Karttunen, Aug 23 2014

STATUS

approved

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Last modified December 22 18:48 EST 2014. Contains 252365 sequences.