A333492 - OEIS

%I #9 Mar 29 2020 05:19:40

%S 1,2,4,8,16,6,64,128,256,18,1024,12,4096,66,20,32768,65536,258,262144,

%T 24,68,1026,4194304,132,16777216,4098,67108864,72,268435456,22,

%U 1073741824,2147483648,1028,65538,80,264,68719476736,262146,4100,144,1099511627776,70,4398046511104

%N Position of first appearance of n in A271410 (LCM of binary indices).

%C A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.

%H Giovanni Resta, <a href="/A333492/b333492.txt">Table of n, a(n) for n = 1..1000</a>

%e The sequence together with the corresponding binary expansions and binary indices begins:

%e       1:                 1 ~ {1}

%e       2:                10 ~ {2}

%e       4:               100 ~ {3}

%e       8:              1000 ~ {4}

%e      16:             10000 ~ {5}

%e       6:               110 ~ {2,3}

%e      64:           1000000 ~ {7}

%e     128:          10000000 ~ {8}

%e     256:         100000000 ~ {9}

%e      18:             10010 ~ {2,5}

%e    1024:       10000000000 ~ {11}

%e      12:              1100 ~ {3,4}

%e    4096:     1000000000000 ~ {13}

%e      66:           1000010 ~ {2,7}

%e      20:             10100 ~ {3,5}

%e   32768:  1000000000000000 ~ {16}

%e   65536: 10000000000000000 ~ {17}

%e     258:         100000010 ~ {2,9}

%t bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];

%t q=Table[LCM@@bpe[n],{n,10000}];

%t Table[Position[q,i][[1,1]],{i,First[Split[Union[q],#1+1==#2&]]}]

%Y The version for prime indices is A330225.

%Y The version for standard compositions is A333225.

%Y Let q(k) be the binary indices of k:

%Y - The sum of q(k) is A029931(k).

%Y - The elements of q(k) are row k of A048793.

%Y - The product of q(k) is A096111(k).

%Y - The LCM of q(k) is A271410(k).

%Y - The GCD of q(k) is A326674(k).

%Y GCD of prime indices is A289508.

%Y LCM of prime indices is A290103.

%Y LCM of standard compositions is A333226.

%Y Cf. A000120, A066099, A070939, A074761, A076078, A124767, A285572, A324837, A328219, A328451, A331579, A333227.

%K nonn

%O 1,2

%A _Gus Wiseman_, Mar 28 2020

%E Terms a(23) and beyond from _Giovanni Resta_, Mar 29 2020