A007094 Numbers in base 8. (Formerly M0498)

0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 34, 35, 36, 37, 40, 41, 42, 43, 44, 45, 46, 47, 50, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 65, 66, 67, 70, 71, 72, 73, 74, 75, 76, 77, 100, 101, 102, 103, 104, 105, 106, 107, 110, 111

Offset

0,3

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, Octal

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/8) if n == 0 (mod 8); a(n) = a(n-1) + 1 otherwise. - Benoit Cloitre, Dec 22 2002

G.f.: sum(d>=0, 10^d*(x^(8^d) +2*x^(2*8^d) +3*x^(3*8^d) +4*x^(4*8^d) +5*x^(5*8^d) +6*x^(6*8^d) +7*x^(7*8^d)) * (1-x^(8^d)) / ((1-x^(8^(d+1)))*(1-x))). - Robert Israel, Aug 03 2014

Maple

A007094 := proc(n) local l: if(n=0)then return 0: fi: l:=convert(n, base, 8): return op(convert(l, base, 10, 10^nops(l))): end: seq(A007094(n), n=0..66); # Nathaniel Johnston, May 06 2011

Mathematica

Table[FromDigits[IntegerDigits[n, 8]], {n, 0, 70}]

Prog

(PARI) a(n)=if(n<1, 0, if(n%8, a(n-1)+1, 10*a(n/8)))
(PARI) apply( A007094(n)=fromdigits(digits(n, 8)), [0..77]) \\ M. F. Hasler, Nov 18 2019
(Haskell)
a007094 0 = 0
a007094 n = 10 * a007094 n' + m where (n', m) = divMod n 8
-- Reinhard Zumkeller, Aug 29 2013
(Python)
def a(n): return int(oct(n)[2:])
print([a(n) for n in range(74)]) # Michael S. Branicky, Jun 28 2021

Crossrefs

Cf. A057104; A000042 (base 1), A007088 (base 2), A007089 (base 3), A007090 (base 4), A007091 (base 5), A007092 (base 6), A007093 (base 7), A007095 (base 9).

Sequence in context: A039207 A272576 A039155 * A000433 A031492 A350076

Adjacent sequences: A007091 A007092 A007093 * A007095 A007096 A007097

Keyword

nonn,easy,base

Author

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

Status

approved