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%I #5 Mar 21 2020 16:35:22
%S 1,2,4,8,16,18,64,34,36,66,1024,68,4096,258,132,136,65536,146,262144,
%T 264,516,4098
%N Position of first appearance of n in A124758 (products of compositions in standard order).
%C A composition of n is a finite sequence of positive integers summing to n. The k-th composition in standard order (row k of A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again.
%e The list of terms together with the corresponding compositions begins:
%e 1: (1)
%e 2: (2)
%e 4: (3)
%e 8: (4)
%e 16: (5)
%e 18: (3,2)
%e 64: (7)
%e 34: (4,2)
%e 36: (3,3)
%e 66: (5,2)
%e 1024: (11)
%e 68: (4,3)
%e 4096: (13)
%e 258: (7,2)
%e 132: (5,3)
%e 136: (4,4)
%e 65536: (17)
%e 146: (3,3,2)
%e 262144: (19)
%e 264: (5,4)
%t stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
%t q=Table[Times@@stc[n],{n,1000}];
%t Table[Position[q,i][[1,1]],{i,First[Split[Union[q],#1+1==#2&]]}]
%Y The product of prime indices is A003963.
%Y The sum of binary indices is A029931.
%Y The sum of prime indices is A056239.
%Y Sums of compositions in standard order are A070939.
%Y The product of binary indices is A096111.
%Y All terms belong to A114994.
%Y Products of compositions in standard order are A124758.
%Y Cf. A000120, A048793, A066099, A164894, A233249, A233564, A272919, A326674, A333217, A333219, A333220, A333223.
%K nonn,more
%O 1,2
%A _Gus Wiseman_, Mar 20 2020
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