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Search: id:A036554
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| A036554 |
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Numbers n such that their binary representation ends in odd number of zeros. |
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+0
32
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| 2, 6, 8, 10, 14, 18, 22, 24, 26, 30, 32, 34, 38, 40, 42, 46, 50, 54, 56, 58, 62, 66, 70, 72, 74, 78, 82, 86, 88, 90, 94, 96, 98, 102, 104, 106, 110, 114, 118, 120, 122, 126, 128, 130, 134, 136, 138, 142, 146, 150, 152, 154, 158, 160, 162, 166, 168, 170, 174
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also n such that A035263(n)=0 or A050292(n)==A050292(n-1).
Indices of even numbers in A033485. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Mar 16 2004
a(n) is an odious number (see A000069) for n odd; a(n) is an evil number (see A001969) for n even. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Mar 16 2004
Indices of even numbers in A007913, in A001511. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Mar 27 2004
This sequence consists of the increasing values of n such that A097357(n) is even. - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Aug 14 2004
Numbers with an odd number of 2's in their prime factorization (e.g. 8 = 2*2*2). - Mark Dow (dow(AT)uoregon.edu), Sep 04 2007
Equals the set of natural numbers not in A003159 or A141290. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 22 2008
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REFERENCES
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L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., Representations for a special sequence, Fib. Quart., 10 (1972), 499-518, 550 (see d(n) on page 501).
Clark Kimberling, Complementary Equations, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.4.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
A. S. Fraenkel, Home Page
A. S. Fraenkel, New games related to old and new sequences, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 4, Paper G6, 2004.
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FORMULA
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a(n) = A003158(n) - n + 1 = A003157(n) - n . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Feb 22 2004
Values of k such that A091297(k) = 2 . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Feb 25 2004
a(n) = A003156(n) + n. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Apr 10 2004
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MATHEMATICA
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f[n_Integer] := Block[{k = n, c = 0}, While[ EvenQ[k], c++; k /= 2]; c]; Select[ Range[185], OddQ[ f[ # ]] & ] (* Or *)
a[n_] := a[n] = If[n < 2, 1, n - a[Floor[n/2]]]; t = Table[a[n], {n, 1, 300}]; Union[ Select[t, t[[ # ]] == t[[ # - 1]] & ]]
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CROSSREFS
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Indices of odd numbers in A007814. Subsequence of A036552. Complement of A003159. Also double of A003159.
Cf. A003157 A003158 A003159.
a(n) = A079523(n)+1 = A072939(n)-1 = A056196(n)/4.
Cf. A141290.
Sequence in context: A075332 A141105 A047395 this_sequence A084909 A038619 A118257
Adjacent sequences: A036551 A036552 A036553 this_sequence A036555 A036556 A036557
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Tom Verhoeff (Tom.Verhoeff(AT)acm.org)
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EXTENSIONS
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More terms from Mark Dow (dow(AT)uoregon.edu), Sep 04 2007
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