A007092 Numbers in base 6.

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

Author

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

Keywords

• nonn
• easy
• base

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.

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).

Programs

Haskell

a007092 0 = 0
a007092 n = 10 * a007092 n' + m where (n', m) = divMod n 6
-- Reinhard Zumkeller, Mar 06 2015

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}]

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

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