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Search: id:A117632
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| A117632 |
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Number of 1's required to build n using {+,T} and parentheses, where T(i) = i(i+1)/2. |
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+0
1
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| 1, 2, 2, 3, 4, 2, 3, 4, 4, 3, 4, 4, 5, 6, 4, 5, 6, 6, 7, 6, 2, 3, 4, 4, 5, 6, 4, 3, 4, 5, 4, 5, 6, 5, 6, 4, 5, 6, 6, 7, 8, 4, 5, 6, 4, 5, 6, 6, 5, 6, 6, 7, 8, 8, 3, 4, 5, 5, 6, 7, 5, 6, 7, 7, 8, 4
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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W. A. Beyer, M. L. Stein and S. M. Ulam, The Notion of Complexity. Report LA-4822, Los Alamos Scientific Laboratory of the University of California, Los Alamos, NM, December 1971.
R. K. Guy, Some suspiciously simple sequences, Amer. Math. Monthly 93 (1986), 186-190; 94 (1987), 965; 96 (1989), 905.
R. K. Guy, Unsolved Problems Number Theory, Sect. F26.
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LINKS
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Ed Pegg, Jr., Integer Complexity.
Eric Weisstein's World of Mathematics, Integer Complexity.
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EXAMPLE
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a(1) = 1 because "1" has a single 1.
a(2) = 2 because "1+1" has two 1's.
a(3) = 2 because 3 = T(1+1) has two 1's.
a(6) = 2 because 6 = T(T(1+1)).
a(10) = 3 because 10 = T(T(1+1)+1).
a(12) = 4 because 12 = T(T(1+1)) + T(T(1+1)).
a(15) = 4 because 15 = T(T(1+1)+1+1)).
a(21) = 2 because 21 = T(T(T(1+1))).
a(28) = 3 because 28 = T(T(T(1+1))+1).
a(55) = 3 because 55 = T(T(T(1+1)+1)).
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CROSSREFS
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See also A023361 = number of compositions into sums of triangular numbers, A053614 = numbers that are not the sum of triangular numbers. Iterated triangular numbers: A050536, A050542, A050548, A050909, A007501.
Cf. A000217, A005245, A005520, A003313, A076142, A076091, A061373, A005421, A023361, A053614, A064097, A025280, A003037, A099129, A050536, A050542, A050548, A050909, A007501.
Sequence in context: A119473 A002122 A105689 this_sequence A127731 A098223 A114892
Adjacent sequences: A117629 A117630 A117631 this_sequence A117633 A117634 A117635
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KEYWORD
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nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 08 2006
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EXTENSIONS
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I do not know how many of these entries have been proved to be minimal. - njas, Apr 15 2006
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