login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A007090 Numbers in base 4.
(Formerly M0900)
314
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 (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
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)))
(PARI) A007090(n)=sum(i=1, #n=digits(n, 4), n[i]*10^(#n-i)) \\ M. F. Hasler, Jul 25 2015 (Corrected by Jinyuan Wang, Oct 02 2019)
(PARI) apply( A007090(n)=fromdigits(digits(n, 4)), [0..66]) \\ M. F. Hasler, Nov 18 2019
(Haskell)
a007090 0 = 0
a007090 n = 10 * a007090 n' + m where (n', m) = divMod n 4
-- Reinhard Zumkeller, Apr 08 2013, Aug 11 2011
CROSSREFS
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.
Sequence in context: A288657 A055655 A276326 * A102859 A069967 A061909
KEYWORD
nonn,easy,base
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 06:05 EDT 2024. Contains 370952 sequences. (Running on oeis4.)