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Search: id:A007090
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| A007090 |
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Numbers in base 4.
(Formerly M0900)
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+0
28
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| 0, 1, 2, 3, 10, 11, 12, 13, 20, 21, 22, 23, 30, 31, 32, 33, 100, 101, 102, 103, 110, 111, 112, 113, 120, 121, 122, 123, 130, 131, 132, 133, 200, 201, 202, 203, 210, 211, 212, 213, 220, 221, 222, 223, 230, 231, 232, 233, 300, 301, 302, 303, 310, 311, 312, 313, 320
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Contribution from Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jun 25 2009: (Start)
Nonnegative integers with no decimal digit > 3.
Thus nonnegative integers in base 10 whose tripling (trebling) by normal addition or multiplication requires no carry operation. (End)
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
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a(n)=Sum{d(i)*10^i: i=0, 1, ..., m}, where Sum{d(i)*4^i: i=0, 1, ..., m} is the base 4 representation of n.
a(0)=0 a(n)=10*a(n/4) if n==0 (mod 4) a(n)=a(n-1)+1 otherwise. - Benoit Cloitre, Dec 22, 2002
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MATHEMATICA
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Table[ FromDigits[ IntegerDigits[n, 4]], {n, 0, 60}]
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PROGRAM
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(PARI) a(n)=if(n<1, 0, if(n%4, a(n-1)+1, 10*a(n/4)))
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CROSSREFS
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Cf. A007608, A000042, A007088, A007089, A007091, A007092, A007093, A007094 & A007095.
Sequence in context: A141670 A074068 A055655 this_sequence A102859 A123977 A069967
Adjacent sequences: A007087 A007088 A007089 this_sequence A007091 A007092 A007093
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KEYWORD
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nonn,base
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
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