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A023717
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Numbers with no 3's in base 4 expansion.
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4
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0, 1, 2, 4, 5, 6, 8, 9, 10, 16, 17, 18, 20, 21, 22, 24, 25, 26, 32, 33, 34, 36, 37, 38, 40, 41, 42, 64, 65, 66, 68, 69, 70, 72, 73, 74, 80, 81, 82, 84, 85, 86, 88, 89, 90, 96, 97, 98, 100, 101, 102, 104, 105, 106, 128, 129, 130, 132, 133
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| A032925 is the intersection of this sequence and A023705; cf. A179888. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 31 2010]
Fixed point of the morphism : 0-> 0,1,2 ; 1-> 4,5,6 ; 2-> 8,9,10 ; ...; n-> 4n,4n+1,4n+2 . - From DELEHAM Philippe, Oct 22 2011.
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LINKS
| R. Zumkeller, Table of n, a(n) for n = 0..10000 [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 31 2010]
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FORMULA
| a(n)=Sum{d(i)*4^i: i=0, 1, ..., m}, where Sum{d(i)*3^i: i=0, 1, ..., m} is the base 3 representation of n. - Clark Kimberling (ck6(AT)evansville.edu)
a(3n)=4a(n); a(3n+1)=4a(n)+1; a(3n+2)=4a(n)+2; a(n)=4*a(floor(n/3))+n-3*floor(n/3) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 27 2003
a(n)=Sum_k>=0 {A030341(n,k)*4^k}. - From DELEHAM Philippe, Oct 22 2011.
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MATHEMATICA
| Select[ Range[ 0, 140 ], (Count[ IntegerDigits[ #, 4 ], 3 ]==0)& ]
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PROG
| (PARI) a(n)=if(n<1, 0, if(n%3, a(n-1)+1, 4*a(n/3))) or a(n)=if(n<1, 0, 4*a(floor(n/3))+n-3*floor(n/3))
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CROSSREFS
| Sequence in context: A095775 A035063 A004128 * A171599 A043687 A087118
Adjacent sequences: A023714 A023715 A023716 * A023718 A023719 A023720
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KEYWORD
| nonn,base,easy
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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