A223909 Numbers for which the maximal run of 1's in their binary representation contains odd number of 1's.

1, 2, 4, 5, 7, 8, 9, 10, 14, 16, 17, 18, 20, 21, 23, 28, 29, 31, 32, 33, 34, 36, 37, 39, 40, 41, 42, 46, 55, 56, 57, 58, 59, 62, 64, 65, 66, 68, 69, 71, 72, 73, 74, 78, 80, 81, 82, 84, 85, 87, 92, 93, 95, 103, 110, 112, 113, 114, 115, 116, 117, 118, 119, 124

Offset: 1

Author

Vladimir Shevelev, Mar 29 2013

Keywords

• nonn
• base

Comments

We call these numbers "maxodious".

If a(n) is in the sequence, then 2^k*a(n) is in the sequence. If a(n)==0 (mod 4) is in the sequence, then a(n)+1 is in the sequence. If a(n)==0 (mod 8) is in the sequence, then a(n)+1, a(n)+2 are in the sequence.

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000069, A001969, A038374.

Programs

Mathematica

Select[Range[500],OddQ[Max[Map[Count[#,1]&,Split[IntegerDigits[#,2]]]]]&] (* Peter J. C. Moses, Mar 29 2013 *)

PARI

A038374(n)=n>>=valuation(n,2);if(n<2,return(n)); my(e=valuation(n+1,2)); max(e, A038374(n>>e))
is(n)=A038374(n)%2 \\ Charles R Greathouse IV, Jan 12 2014

Formula

Numbers n such that A038374(n) is odd. - Charles R Greathouse IV, Jan 12 2014