

A223909


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


2



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
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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



