

A207901


Let S_k denote the first 2^k terms of this sequence and let b_k be the smallest positive integer that is not in S_k, also let R_k equal S_k read in reverse order; then the numbers b_k*R_k are the next 2^k terms.


17



1, 2, 6, 3, 12, 24, 8, 4, 20, 40, 120, 60, 15, 30, 10, 5, 35, 70, 210, 105, 420, 840, 280, 140, 28, 56, 168, 84, 21, 42, 14, 7, 63, 126, 378, 189, 756, 1512, 504, 252, 1260, 2520, 7560, 3780, 945, 1890, 630, 315, 45, 90, 270, 135, 540, 1080, 360, 180, 36, 72, 216
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OFFSET

0,2


COMMENTS

A permutation of the positive integers (but please note the starting offset: 0indexed).
This sequence is a variant of A052330.
Shares with A064736, A302350, etc. the property that a(n) is either a divisor or a multiple of a(n+1).  Peter Munn, Apr 11 2018 on SeqFanlist. Note: A302781 is another such "divisorormultiple permutation" satisfying the same property.  Antti Karttunen, Apr 14 2018
The offset is 0 since S_0 = {1} denotes the first 2^0 = 1 terms.  Daniel Forgues, Apr 13 2018
This is "FermiDirac piano played with Gray code", as indicated by Peter Munn's Apr 11 2018 formula. Compare also to A303771 and A302783.  Antti Karttunen, May 16 2018


LINKS

Antti Karttunen, Table of n, a(n) for n = 0..8191 (first 1024 terms from Paul D. Hanna)
Michel Marcus, Peter Munn, et al, Discussion on SeqFanlist
Index entries for sequences that are permutations of the natural numbers


FORMULA

a(n) = A052330(A003188(n)).  Peter Munn, Apr 11 2018
a(n) = A302781(A302843(n)) = A302783(A064706(n)).  Antti Karttunen, Apr 16 2018
a(n+1) = A059897(a(n), A050376(A001511(n+1))).  Peter Munn, Apr 01 2019


EXAMPLE

Start with [1]; appending 2*[1] results in [1,2];
appending 3*[2,1] results in [1,2, 6,3];
appending 4*[3,6,2,1] results in [1,2,6,3, 12,24,8,4];
appending 5*[4,8,24,12,3,6,2,1]
results in [1,2,6,3,12,24,8,4, 20,40,120,60,15,30,10,5];
next append 7*[5,10,30,15,60,120,40,20,4,8,24,12,3,6,2,1],
multiplying by 7 since 6 is already found in the previous terms.
Each new factor is in A050376: [2,3,4,5,7,9,11,13,16,17,19,23,25,29,...].
Continue in this way to generate all the terms of this sequence.


MATHEMATICA

a = {1}; Do[a = Join[a, Reverse[a]*Min[Complement[Range[Max[a] + 1], a]]], {n, 1, 6}]; a (* Ivan Neretin, May 09 2015 *)


PROG

(PARI) {A050376(n)= local(m, c, k, p); n; if(n<=0, 2*(n==0), c=0; m=2; while( c<n, m++; if( isprime(m)  ( (k=ispower(m, , &p))&&isprime(p)&& k ==2^valuation(k, 2) ), c++)); m)}
{a(n)=local(A=[1]); n++; for(n=1, 10, A=concat(A, A050376(n1)*Vec(Polrev(A)))); A[n]}
for(n=0, 63, print1(a(n), ", ")) \\ edited for offsets by Michel Marcus, Apr 04 2019
(PARI)
up_to_e = 13;
v050376 = vector(up_to_e);
A050376(n) = v050376[n];
ispow2(n) = (n && !bitand(n, n1));
i = 0; for(n=1, oo, if(ispow2(isprimepower(n)), i++; v050376[i] = n); if(i == up_to_e, break));
A052330(n) = { my(p=1, i=1); while(n>0, if(n%2, p *= A050376(i)); i++; n >>= 1); (p); };
A003188(n) = bitxor(n, n>>1);
A207901(n) = A052330(A003188(n)); \\ Antti Karttunen, Apr 13 2018


CROSSREFS

Cf. A001511, A003188, A052330, A050376, A059897, A064706, A302029 (inverse), A302843.
Cf. A064736, A281978, A282291, A302350, A302781, A302783, A303751, A303771, A304085, A304531, A304755 for other divisorormultiple permutations or conjectured permutations.
Cf. A302033 (a squarefree analog), A304745.
Sequence in context: A063929 A276158 A092393 * A054619 A054618 A120859
Adjacent sequences: A207898 A207899 A207900 * A207902 A207903 A207904


KEYWORD

nonn,look


AUTHOR

Paul D. Hanna, Feb 21 2012


EXTENSIONS

Offset changed from 1 to 0 by Antti Karttunen, Apr 13 2018


STATUS

approved



