A303789 a(n) = Sum_{i=0..m} d(i)*6^i, where Sum_{i=0..m} d(i)*7^i is the base-7 representation of n.

0, 1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 12, 12, 13, 14, 15, 16, 17, 18, 18, 19, 20, 21, 22, 23, 24, 24, 25, 26, 27, 28, 29, 30, 30, 31, 32, 33, 34, 35, 36, 36, 37, 38, 39, 40, 41, 42, 36, 37, 38, 39, 40, 41, 42, 42, 43, 44, 45, 46, 47, 48, 48, 49, 50, 51, 52, 53, 54, 54, 55

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Example

19 = 25_7, so a(19) = 2*6 + 5 = 17.
20 = 26_7, so a(20) = 2*6 + 6 = 18.
21 = 30_7, so a(21) = 3*6 + 0 = 18.
22 = 31_7, so a(22) = 3*6 + 1 = 19.

Prog

(Ruby)
def f(k, ary)
  (0..ary.size - 1).inject(0){|s, i| s + ary[i] * k ** i}
end
def A(k, n)
  (0..n).map{|i| f(k, i.to_s(k + 1).split('').map(&:to_i).reverse)}
end
p A(6, 100)
(PARI) a(n) = fromdigits(digits(n, 7), 6); \\ Michel Marcus, May 02 2018

Crossrefs

Sum_{i=0..m} d(i)*b^i, where Sum_{i=0..m} d(i)*(b+1)^i is the base (b+1) representation of n: A065361 (b=2), A215090 (b=3), A303787 (b=4), A303788 (b=5), this sequence (b=6).

Cf. A037470.

Sequence in context: A245337 A006164 A053758 * A145569 A213851 A172475

Adjacent sequences: A303786 A303787 A303788 * A303790 A303791 A303792

Keyword

nonn,base

Author

Seiichi Manyama, Apr 30 2018

Status

approved