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A333219 Heinz number of the n-th composition in standard order. 50
1, 2, 3, 4, 5, 6, 6, 8, 7, 10, 9, 12, 10, 12, 12, 16, 11, 14, 15, 20, 15, 18, 18, 24, 14, 20, 18, 24, 20, 24, 24, 32, 13, 22, 21, 28, 25, 30, 30, 40, 21, 30, 27, 36, 30, 36, 36, 48, 22, 28, 30, 40, 30, 36, 36, 48, 28, 40, 36, 48, 40, 48, 48, 64, 17, 26, 33, 44 (list; graph; refs; listen; history; text; internal format)
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).

LINKS

Table of n, a(n) for n=1..68.

FORMULA

A056239(a(n)) = A070939(n).

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).

A partial inverse is A333220. See also A233249.

Cf. A048793, A056239, A066099, A112798, A114994, A124767, A213925, A225620, A228351, A233564, A272919, A333218.

Sequence in context: A153249 A097621 A017851 * A265537 A061468 A084766

Adjacent sequences:  A333216 A333217 A333218 * A333220 A333221 A333222

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 16 2020

STATUS

approved

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Last modified September 18 23:06 EDT 2020. Contains 337174 sequences. (Running on oeis4.)