A227737 n occurs as many times as there are runs in binary representation of n.

1, 2, 2, 3, 4, 4, 5, 5, 5, 6, 6, 7, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 14, 14, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 24, 24, 25, 25, 25, 26, 26, 26, 26

Offset

1,2

Comments

a(n) = the least integer k such that A173318(k) >= n, which implies that each n occurs A005811(n) times.

Although as such quite uninteresting, this sequence is useful for computing irregular tables like A101211, A227736, A227738 and A227739.

Links

Antti Karttunen, Table of n, a(n) for n = 1..5120

Example

1 has one run in its binary representation "1", thus 1 occurs once.
2 has two runs in its binary representation "10", thus 2 occurs twice.
3 has one run in its binary representation "11", thus 3 occurs only once.
4 has two runs in its binary representation "100", thus 4 occurs twice.
5 has three runs in its binary representation "101", thus 5 occurs three times.
The sequence thus begins as 1, 2,2, 3, 4,4, 5,5,5, ...

Mathematica

Table[ConstantArray[n, Length@ Split@ IntegerDigits[n, 2]], {n, 26}] // Flatten (* Michael De Vlieger, May 09 2017 *)
Table[PadRight[{}, Length[Split[IntegerDigits[n, 2]]], n], {n, 40}]//Flatten (* Harvey P. Dale, Jul 23 2021 *)

Prog

(Scheme with Antti Karttunen's IntSeq-library) (define A227737 (LEAST-GTE-I 1 1 A173318))

Crossrefs

Cf. A227740, A227741, A005811, A173318.

Sequence in context: A194175 A194241 A089575 * A194177 A348386 A023190

Adjacent sequences: A227734 A227735 A227736 * A227738 A227739 A227740

Keyword

nonn,base

Author

Antti Karttunen, Jul 25 2013

Status

approved