A303787 a(n) = Sum_{i=0..m} d(i)*4^i, where Sum_{i=0..m} d(i)*5^i is the base-5 representation of n.

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

Offset

0,3

Links

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

Example

13 = 23_5, so a(13) = 2*4 + 3 = 11.
14 = 24_5, so a(14) = 2*4 + 4 = 12.
15 = 30_5, so a(15) = 3*4 + 0 = 12.
16 = 31_5, so a(16) = 3*4 + 1 = 13.

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(4, 100)
(PARI) a(n) = fromdigits(digits(n, 5), 4); \\ Michel Marcus, May 02 2018
(Julia)
function a(n)
    m, r, b = n, 0, 1
    while m > 0
        m, q = divrem(m, 5)
        r += b * q
        b *= 4
    end
r end; [a(n) for n in 0:73] |> println # Peter Luschny, Jan 03 2021

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), this sequence (b=4), A303788 (b=5), A303789 (b=6).

Cf. A020654, A037459.

Sequence in context: A210436 A003004 A120507 * A090223 A366870 A171974

Adjacent sequences: A303784 A303785 A303786 * A303788 A303789 A303790

Keyword

nonn,base

Author

Seiichi Manyama, Apr 30 2018

Status

approved