A007092 Numbers in base 6. (Formerly M0532)

0, 1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, 30, 31, 32, 33, 34, 35, 40, 41, 42, 43, 44, 45, 50, 51, 52, 53, 54, 55, 100, 101, 102, 103, 104, 105, 110, 111, 112, 113, 114, 115, 120, 121, 122, 123, 124, 125, 130, 131, 132, 133, 134, 135, 140, 141, 142, 143, 144, 145

Offset

0,3

Comments

Nonnegative integers with no decimal digits > 5. - Karol Bacik, Sep 25 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

Wikipedia, Senary

R. G. Wilson, V, Letter to N. J. A. Sloane, Sep. 1992

Index entries for 10-automatic sequences.

Formula

a(0)=0, a(n) = 10*a(n/6) if n==0 (mod 6), and a(n) = a(n-1)+1 otherwise. - Benoit Cloitre, Dec 22 2002

a(n) = Sum{d(i)*10^i: i=0,1,...,m}, where Sum{d(i)*6^i: i=1,2,...,m} = n, and d(i) in {0,1,...,5}. - Karol Bacik, Sep 25 2012

Maple

A007092 := proc(n) local l: if(n=0)then return 0: fi: l:=convert(n, base, 6): return op(convert(l, base, 10, 10^nops(l))): end: seq(A007092(n), n=0..59); # Nathaniel Johnston, May 06 2011

Mathematica

Table[ FromDigits[ IntegerDigits[n, 6]], {n, 0, 65}]

Prog

(PARI) a(n)=if(n%6, a(n-1)+1, if(n, 10*a(n/6), 0))  \\ corrected by Charles R Greathouse IV, Sep 25 2012
(PARI) a(n)=n=digits(n, 6); n[1]=Str(n[1]); eval(concat(n)) \\ Charles R Greathouse IV, Sep 25 2012
(PARI) apply( A007092(n)=fromdigits(digits(n, 6)), [0..66]) \\ M. F. Hasler, Nov 18 2019
(Haskell)
a007092 0 = 0
a007092 n = 10 * a007092 n' + m where (n', m) = divMod n 6
-- Reinhard Zumkeller, Mar 06 2015

Crossrefs

Cf. A000042 (base 1), A007088 (base 2), A007089 (base 3), A007090 (base 4), A007091 (base 5), A007093 (base 7), A007094 (base 8), A007095 (base 9).

Sequence in context: A261039 A266117 A037473 * A241213 A362931 A375514

Adjacent sequences: A007089 A007090 A007091 * A007093 A007094 A007095

Keyword

nonn,easy,base

Author

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

Status

approved