A303788 a(n) = Sum_{i=0..m} d(i)*5^i, where Sum_{i=0..m} d(i)*6^i is the base-6 representation of n.

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

Offset

0,3

Links

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

Example

16 = 24_6, so a(16) = 2*5 + 4 = 14.
17 = 25_6, so a(17) = 2*5 + 5 = 15.
18 = 30_6, so a(18) = 3*5 + 0 = 15.
19 = 31_6, so a(19) = 3*5 + 1 = 16.

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(5, 100)
(PARI) a(n) = fromdigits(digits(n, 6), 5); \\ 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), this sequence (b=5), A303789 (b=6).

Cf. A037465.

Sequence in context: A053757 A256562 A228297 * A366871 A319288 A106744

Adjacent sequences: A303785 A303786 A303787 * A303789 A303790 A303791

Keyword

nonn,base

Author

Seiichi Manyama, Apr 30 2018

Status

approved