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
R. G. Wilson, V, Letter to N. J. A. Sloane, Sep. 1992
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
KEYWORD
nonn,easy,base
AUTHOR
STATUS
approved