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A227737 n occurs as many times as there are runs in binary representation of n. 9
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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 A023190 A047783

Adjacent sequences:  A227734 A227735 A227736 * A227738 A227739 A227740

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Jul 25 2013

STATUS

approved

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Last modified August 11 15:12 EDT 2020. Contains 336428 sequences. (Running on oeis4.)