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A007090
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Numbers in base 4.
(Formerly M0900)
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314
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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, 321, 322, 323, 330, 331, 332, 333
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OFFSET
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0,3
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COMMENTS
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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. - Rick L. Shepherd, Jun 25 2009
Interpreted in base 10: a(x)+a(y) = a(z) => x+y = z. The converse is not true in general. - Karol Bacik, Sep 27 2012
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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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LINKS
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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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MAPLE
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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
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Table[ FromDigits[ IntegerDigits[n, 4]], {n, 0, 60}]
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PROG
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(PARI) a(n)=if(n<1, 0, if(n%4, a(n-1)+1, 10*a(n/4)))
(Haskell)
a007090 0 = 0
a007090 n = 10 * a007090 n' + m where (n', m) = divMod n 4
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CROSSREFS
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Cf. A007608, A000042, A007088 (base 2), A007089 (base 3), A007091 (base 5), A007092 (base 6), A007093 (base 7), A007094 (base 8), A007095 (base 9), A193890, A107715.
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KEYWORD
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nonn,easy,base
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AUTHOR
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STATUS
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approved
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