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 A007090 Numbers in base 4. (Formerly M0900) 85
 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 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) 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 (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) 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 Adjacent sequences:  A007087 A007088 A007089 * A007091 A007092 A007093 KEYWORD nonn,easy,base AUTHOR STATUS approved

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Last modified September 19 01:52 EDT 2020. Contains 337175 sequences. (Running on oeis4.)