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

Author

Seiichi Manyama, Apr 30 2018

Keywords

• nonn
• base

Examples

			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.
		

Links

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

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.

Programs

PARI

a(n) = fromdigits(digits(n, 7), 6); \\ Michel Marcus, May 02 2018

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)