OFFSET
1,2
COMMENTS
Includes all positive integers.
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.
The Heinz number of a composition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {} 15: {2,3} 25: {3,3}
2: {1} 20: {1,1,3} 30: {1,2,3}
3: {2} 15: {2,3} 30: {1,2,3}
4: {1,1} 18: {1,2,2} 40: {1,1,1,3}
5: {3} 18: {1,2,2} 21: {2,4}
6: {1,2} 24: {1,1,1,2} 30: {1,2,3}
6: {1,2} 14: {1,4} 27: {2,2,2}
8: {1,1,1} 20: {1,1,3} 36: {1,1,2,2}
7: {4} 18: {1,2,2} 30: {1,2,3}
10: {1,3} 24: {1,1,1,2} 36: {1,1,2,2}
9: {2,2} 20: {1,1,3} 36: {1,1,2,2}
12: {1,1,2} 24: {1,1,1,2} 48: {1,1,1,1,2}
10: {1,3} 24: {1,1,1,2} 22: {1,5}
12: {1,1,2} 32: {1,1,1,1,1} 28: {1,1,4}
12: {1,1,2} 13: {6} 30: {1,2,3}
16: {1,1,1,1} 22: {1,5} 40: {1,1,1,3}
11: {5} 21: {2,4} 30: {1,2,3}
14: {1,4} 28: {1,1,4} 36: {1,1,2,2}
MATHEMATICA
stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
Table[Times@@Prime/@stc[n], {n, 0, 100}]
CROSSREFS
The length of the k-th composition in standard order is A000120(k).
The sum of the k-th composition in standard order is A070939(k).
The maximum of the k-th composition in standard order is A070939(k).
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 16 2020
STATUS
approved