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Search: id:A007378
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| A007378 |
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a(n), n>=2, is smallest positive integer which is consistent with sequence being monotonically increasing and satisfying a(a(n)) = 2n.
(Formerly M2317)
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+0
11
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| 3, 4, 6, 7, 8, 10, 12, 13, 14, 15, 16, 18, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 36, 38, 40, 42, 44, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 97, 98, 99, 100, 101, 102, 103
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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This is the unique monotonic sequence {a(n)}, n>=2, satisfying a(a(n)) = 2n.
May also be defined by: a(n), n=2,3,4,..., is smallest positive integer greater than a(n-1) which is consistent with the condition "n is a member of the sequence if and only if a(n) is an even number >= 4". - njas, Feb 23 2003
A monotone sequence satisfying a^(k+1)(n) = mn is unique if m=2, k >= 0 or if (k,m) = (1,3). See A088720. - C.L.Mallows (colinm(AT)research.avayalabs.com), Oct 16 2003
Numbers (greater than 2) whose binary representation starts with "11" or ends with "0". - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 17 2006
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REFERENCES
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J.-P. Allouche, N. Rampersad and J. Shallit, On integer sequences whose first iterates are linear, Aequationes Math. 69 (2005), 114-127
J.-P. Allouche and J. Shallit, The ring of k-regular sequences, II, Theoret. Computer Sci., 307 (2003), 3-29.
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LINKS
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J.-P. Allouche and J. Shallit, The Ring of k-regular Sequences, II
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence (math.NT/0305308)
J. Shallit, k-regular Sequences
R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
Index entries for sequences of the a(a(n)) = 2n family
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FORMULA
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a(2^i + j) = 3*2^(i-1) + j, 0<=j<2^(i-1); a(3*2^(i-1) + j) = 2^(i+1) + 2*j, 0<=j<2^(i-1).
a(3*2^k + j) = 4*2^k + 3j/2 + |j|/2, k>=0, -2^k <= j < 2^k. - njas, Feb 23 2003
a(2*n+1) = a(n+1)+a(n), a(2*n) = 2*a(n). a(n) = n+A060973(n). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Mar 01 2003
G.f. -x/(1-x) + x/(1-x)^2 * (2 + sum(k>=0, t^2(t-1), t=x^2^k)). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 12 2003
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CROSSREFS
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Cf. A003605. Equals A080653 + 2.
This sequence, A079905, A080637 and A080653 are all essentially the same.
Cf. A088720.
Adjacent sequences: A007375 A007376 A007377 this_sequence A007379 A007380 A007381
Sequence in context: A022846 A083922 A039042 this_sequence A087758 A105454 A127260
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KEYWORD
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nonn,easy,nice
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AUTHOR
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C. L. Mallows (colinm(AT)research.avayalabs.com)
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EXTENSIONS
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More terms from Matthew Vandermast (ghodges14(AT)comcast.net) and Vladeta Jovovic (vladeta(AT)Eunet.yu), Mar 01 2003
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