A249102 Numbers with no 1's in base-7 expansion.

0, 2, 3, 4, 5, 6, 14, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 98, 100, 101, 102, 103, 104, 112, 114, 115, 116, 117, 118, 119, 121, 122, 123, 124, 125, 126, 128, 129, 130, 131, 132, 133

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Example

14_10 = 20_7, 16_10 = 22_10, 17_10 = 23_7.
14 in base 7 is 20, which contains no 1s, so 14 is in the sequence.
15 in base 7 is 21, which contains one 1, so 15 is not in the sequence.
16 in base 7 is 22, so 16 is in the sequence.

Mathematica

Select[Range[0, 200], FreeQ[IntegerDigits[#, 7], 1] &] (* Seidov *)
Select[Range[0, 139], DigitCount[#, 7, 1] == 0 &] (* Alonso del Arte, Oct 26 2014 *)

Prog

(PARI) fromdigits(v, b=10)=subst(Pol(v), 'x, b) \\ needed for gp < 2.63 or so
a(n)=a(n)=fromdigits(apply(k->if(k, k+1, 0), digits(n, 6)), 7) \\ Charles R Greathouse IV, Oct 30 2014

Crossrefs

Subsequence of A047306. Cf. A023721, A023725, A023729, A023733, A005823. This sequence has no terms in common with A016993.

Sequence in context: A204896 A334733 A039016 * A250047 A084830 A116044

Adjacent sequences: A249099 A249100 A249101 * A249103 A249104 A249105

Keyword

base,nonn

Author

Zak Seidov, Oct 21 2014

Status

approved