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

1,2

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

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000069, A001969, A038374.

Sequence in context: A285423 A173025 A203463 * A010392 A095042 A010423

Adjacent sequences: A223906 A223907 A223908 * A223910 A223911 A223912

Keyword

nonn,base

Author

Vladimir Shevelev, Mar 29 2013

Status

approved