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A023717 Numbers with no 3's in base 4 expansion. 8
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; text; internal format)
OFFSET

0,3

COMMENTS

A032925 is the intersection of this sequence and A023705; cf. A179888. -Reinhard Zumkeller, 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 . - Philippe Deléham, Oct 22 2011.

LINKS

R. Zumkeller, Table of n, a(n) for n = 0..10000

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

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, Apr 27 2003

a(n)=Sum_k>=0 {A030341(n,k)*4^k}. - Philippe Deléham, Oct 22 2011.

MATHEMATICA

Select[ Range[ 0, 140 ], (Count[ IntegerDigits[ #, 4 ], 3 ]==0)& ]

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))

(Haskell)

a023717 n = a023717_list !! (n-1)

a023717_list = filter f [0..] where

   f x = x < 3 || (q < 3 && f x') where (x', q) = divMod x 4

-- Reinhard Zumkeller, Apr 18 2015

CROSSREFS

Cf. A032925, A023705, A179888.

Sequence in context: A095775 A035063 A004128 * A171599 A288174 A280998

Adjacent sequences:  A023714 A023715 A023716 * A023718 A023719 A023720

KEYWORD

nonn,base,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified February 22 19:52 EST 2019. Contains 320403 sequences. (Running on oeis4.)