

A129771


Evil odd numbers.


13



3, 5, 9, 15, 17, 23, 27, 29, 33, 39, 43, 45, 51, 53, 57, 63, 65, 71, 75, 77, 83, 85, 89, 95, 99, 101, 105, 111, 113, 119, 123, 125, 129, 135, 139, 141, 147, 149, 153, 159, 163, 165, 169, 175, 177, 183, 187, 189, 195, 197, 201, 207, 209, 215, 219, 221, 225, 231, 235
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OFFSET

1,1


COMMENTS

A heuristic argument suggests that, as n tends to infinity, a(n)/n converges to 4.  Stefan Steinerberger, May 17 2007
These numbers may be called primitive evil numbers because every evil number is a power of twice one of these numbers. Note that the difference between consecutive terms is either 2, 4, or 6.  T. D. Noe, Jun 06 2007
A132680(a(n)) = A132680((a(n)1)/2) + 2.  Reinhard Zumkeller, Aug 26 2007
If m is in the sequence, then so is 2m1 because in binary, m is x1 and 2m1 is x01. Presumably the numbers that generate the whole sequence by application of n > 2n1 are the evil numbers times 4 plus 3.  Ralf Stephan, May 25 2013


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000


FORMULA

a(n) = 2*A000069(n) + 1. a(n) is 1 plus twice odious numbers. a(n) = A128309(n) + 1. a(n) is 1 plus odious even numbers.
a(n) = 4n + O(1).  Charles R Greathouse IV, Mar 21 2013
a(n) = A001969(1+A000069(n)) = A277902(A277823(n)).  Antti Karttunen, Nov 05 2016


MATHEMATICA

Select[Range[300], OddQ[ # ] && EvenQ[DigitCount[ #, 2, 1]] &] (* Stefan Steinerberger, May 17 2007 *)
Select[Range[300], EvenQ[Plus @@ IntegerDigits[ #, 2]] && OddQ[ # ] &]


PROG

(PARI) is(n)=n%2 && hammingweight(n)%2==0 \\ Charles R Greathouse IV, Mar 21 2013
(PARI) a(n)=4*nif(hammingweight(n1)%2, 3, 1) \\ Charles R Greathouse IV, Mar 21 2013


CROSSREFS

This sequence is the intersection of A001969 (Evil numbers: even number of 1's in binary expansion.) and A005408 (The odd numbers: a(n) = 2n+1.) A093688 (Numbers n such that all divisors of n, excluding the divisor 1, have an even number of 1's in their binary expansions) is a subsequence.
Cf. A092246 (odd odious numbers).
Column 2 of A277880, positions of 1's in A277808 (2's in A277822).
Cf. A000069, A128309, A277823, A277902.
Sequence in context: A120695 A103578 A116649 * A209837 A093688 A174688
Adjacent sequences: A129768 A129769 A129770 * A129772 A129773 A129774


KEYWORD

nonn,easy


AUTHOR

Tanya Khovanova, May 16 2007


EXTENSIONS

More terms from Stefan Steinerberger, May 17 2007


STATUS

approved



