A286613 -id:A286613 - cp's OEIS frontend

A286614 Restricted growth sequence transform of A286613.

1, 2, 2, 2, 3, 4, 2, 5, 5, 2, 6, 2, 3, 5, 6, 2, 2, 2, 6, 7, 5, 2, 8, 6, 2, 5, 5, 2, 6, 6, 2, 5, 3, 6, 5, 6, 5, 2, 9, 5, 10, 6, 2, 5, 11, 2, 9, 5, 5, 9, 5, 5, 8, 12, 2, 6, 13, 5, 14, 2, 2, 9, 5, 5, 5, 5, 2, 2, 13, 6, 2, 2, 5, 2, 13, 8, 5, 5, 12, 6, 5, 5, 5, 2, 5, 6, 6, 5, 2, 2, 6, 6, 9, 5, 6, 15, 5, 5, 6, 5

Offset: 0

Antti Karttunen, May 30 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 0..65536

Cf. A286613, A286622.

rgs_transform(invec) = { my(occurrences = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(occurrences,invec[i]), my(pp = mapget(occurrences, invec[i])); outvec[i] = outvec[pp] , mapput(occurrences,invec[i],i); outvec[i] = u; u++ )); outvec; };
write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ This function from Michel Marcus
A048673(n) = (A003961(n)+1)/2;
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ Modified from code of M. F. Hasler
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from Charles R Greathouse IV, Aug 17 2011
A286613(n) = A046523(A048673(A005940(1+n)));
write_to_bfile(0,rgs_transform(vector(65537,n,A286613(n-1))),"b286614.txt");

A244154 Permutation of natural numbers: a(0) = 1, a(1) = 2, a(2n) = A254049(a(n)), a(2n+1) = 3*a(n)-1; composition of A048673 and A005940.

Original entry on oeis.org

1, 2, 3, 5, 4, 8, 13, 14, 6, 11, 18, 23, 25, 38, 63, 41, 7, 17, 28, 32, 39, 53, 88, 68, 61, 74, 123, 113, 172, 188, 313, 122, 9, 20, 33, 50, 46, 83, 138, 95, 72, 116, 193, 158, 270, 263, 438, 203, 85, 182, 303, 221, 424, 368, 613, 338, 666, 515, 858, 563, 1201, 938, 1563, 365, 10, 26, 43, 59, 60

Offset: 0

Antti Karttunen, Jun 27 2014

Note the indexing: the domain starts from 0, while the range excludes zero.
From Antti Karttunen, May 30 2017: (Start)
This sequence can be represented as a binary tree. Each left hand child is obtained by applying A254049(n) when the parent contains n, and each right hand child is obtained by applying A016789(n-1) (i.e., multiply by 3, subtract one) to the parent's contents:
                                     1
                                     |
                  ...................2...................
                 3                                       5
       4......../ \........8                  13......../ \........14
      / \                 / \                 / \                 / \
     /   \               /   \               /   \               /   \
    /     \             /     \             /     \             /     \
   6       11         18       23         25       38         63       41
  7 17   28  32     39  53   88  68     61  74  123  113   172  188  313 122
etc.
This is a mirror image of the tree depicted in A245612.
(End)

Antti Karttunen, Table of n, a(n) for n = 0..8192
Index entries for sequences that are permutations of the natural numbers

Inverse: A244153.

Cf. A005940, A048673, A054429, A243065-A243066, A243505-A243506, A245608, A245610, A245612, A016789, A254049, A285712, A285714, A286613.

(define (A244154 n) (A048673 (A005940 (+ 1 n))))
;; Implementing a new recurrence, with memoization-macro definec:
(definec (A244154 n) (cond ((<= n 1) (+ 1 n)) ((even? n) (A254049 (A244154 (/ n 2)))) (else (+ -1 (* 3 (A244154 (/ (- n 1) 2))))))) ;; Antti Karttunen, May 30 2017

a(n) = A048673(A005940(n+1)).
From Antti Karttunen, May 30 2017: (Start)
a(0) = 1, a(1) = 2, a(2n) = A254049(a(n)), a(2n+1) = 3*a(n)-1.
a(n) = A245612(A054429(n)).
(End)

A285713 a(n) = A046523(A245612(n)).

Original entry on oeis.org

1, 2, 2, 2, 6, 2, 8, 4, 2, 12, 6, 4, 2, 12, 2, 6, 6, 2, 12, 12, 2, 6, 6, 2, 12, 24, 2, 6, 32, 12, 2, 2, 6, 6, 30, 2, 2, 210, 6, 60, 12, 2, 48, 24, 6, 6, 30, 6, 6, 30, 2, 120, 6, 2, 12, 72, 6, 30, 2, 6, 12, 6, 12, 4, 6, 6, 48, 60, 6, 60, 6, 2, 24, 192, 6, 6, 24, 768, 2, 6, 2, 6, 6, 6, 2, 30, 6, 210, 6, 6, 12, 48, 6, 12, 6, 6, 96, 12, 6, 30, 12, 12, 2, 2, 6

Offset: 0

Antti Karttunen, Apr 25 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 0..8191

Cf. A046523, A163511, A245612, A278224, A278531, A285712, A286613.

Cf. A305434 (rgs-transform).

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A048673(n) = (A003961(n)+1)/2;
A254049(n) = A048673((2*n)-1);
A245612(n) = if(n<2,1+n,if(!(n%2),(3*A245612(n/2))-1,A254049(A245612((n-1)/2))));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A285713(n) = A046523(A245612(n)); \\ Antti Karttunen, Jun 01 2018

(define (A285713 n) (A046523 (A245612 n)))

a(n) = A046523(A245612(n)).
a(n) = A278224(A163511(n)).
a(n) = A286613(A054429(n)). - Antti Karttunen, Jun 01 2018

cp's OEIS Frontend

A286614 Restricted growth sequence transform of A286613.

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A244154 Permutation of natural numbers: a(0) = 1, a(1) = 2, a(2n) = A254049(a(n)), a(2n+1) = 3*a(n)-1; composition of A048673 and A005940.

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A285713 a(n) = A046523(A245612(n)).

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