A007093 Numbers in base 7.

0, 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 14, 15, 16, 20, 21, 22, 23, 24, 25, 26, 30, 31, 32, 33, 34, 35, 36, 40, 41, 42, 43, 44, 45, 46, 50, 51, 52, 53, 54, 55, 56, 60, 61, 62, 63, 64, 65, 66, 100, 101, 102, 103, 104, 105, 106, 110, 111, 112, 113, 114, 115, 116, 120

Offset: 0

Author

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

Keywords

• nonn
• easy
• base

References

• Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966. See p. 67.
• 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
• Index entries for 10-automatic sequences.

Crossrefs

Cf. A000042, A007088, A007089, A007090, A007091, A007092, A007094, A007095.

Programs

Maple

A007093 := proc(n) local l: if(n=0)then return 0: fi: l:=convert(n,base,7): return op(convert(l,base,10,10^nops(l))): end: seq(A007093(n),n=0..63); # Nathaniel Johnston, May 06 2011

Mathematica

Table[ FromDigits[ IntegerDigits[n, 7]], {n, 0, 66}]

PARI

a(n)=if(n<1,0,if(n%7,a(n-1)+1,10*a(n/7)))

PARI

a(n) = fromdigits(digits(n, 7)); \\ Michel Marcus, Aug 12 2018

Formula

a(0) = 0, a(n) = 10*a(n/7) if n==0 (mod 7), a(n) = a(n-1)+1 otherwise. - Benoit Cloitre, Dec 22 2002