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A007090 Numbers in base 4.
(Formerly M0900)
59
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; text; internal format)
OFFSET

0,3

COMMENTS

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

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 0..10000

Index entries for 10-automatic sequences.

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

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

MATHEMATICA

Table[ FromDigits[ IntegerDigits[n, 4]], {n, 0, 60}]

PROG

(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

-- Reinhard Zumkeller, Apr 08 2013, Aug 11 2011

(PARI) A007090(n)=sum(i=1, #n==digits(n, 4), n[i]*10^(#n-i)) \\ M. F. Hasler, Jul 25 2015

CROSSREFS

Cf. A007608, A000042, A007088, A007089, A007091, A007092, A007093, A007094, A007095, A193890, A107715.

Sequence in context: A288657 A055655 A276326 * A102859 A069967 A061909

Adjacent sequences:  A007087 A007088 A007089 * A007091 A007092 A007093

KEYWORD

nonn,easy,base

AUTHOR

N. J. A. Sloane, Robert G. Wilson v

STATUS

approved

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Last modified June 22 08:03 EDT 2017. Contains 288605 sequences.