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A007090
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Numbers in base 4.
(Formerly M0900)
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32
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 0..10000
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FORMULA
| 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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MAPLE
| A007090 := proc(n) local l: if(n=0)then return 0: fi: l:=convert(n, base, 4): return op(convert(l, base, 10, 10^nops(l))): end: seq(A007090(n), n=0..54); # Nathaniel Johnston, May 06 2011
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MATHEMATICA
| Table[ FromDigits[ IntegerDigits[n, 4]], {n, 0, 60}]
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PROG
| (PARI) a(n)=if(n<1, 0, if(n%4, a(n-1)+1, 10*a(n/4)))
(Haskell)
import Numeric (showIntAtBase)
import Data.Char (intToDigit)
a007090 n = read $ showIntAtBase 4 intToDigit n "" :: Integer
a007090_list = map a007090 [0..]
-- Reinhard Zumkeller, Aug 11 2011
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CROSSREFS
| Cf. A007608, A000042, A007088, A007089, A007091, A007092, A007093, A007094, A007095.
Cf. A193890, A107715.
Sequence in context: A193729 A074068 A055655 * A102859 A069967 A061909
Adjacent sequences: A007087 A007088 A007089 * A007091 A007092 A007093
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KEYWORD
| nonn,easy,base
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
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