A303789 - OEIS

%I #34 Jun 29 2019 01:39:12

%S 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,

%T 23,24,24,25,26,27,28,29,30,30,31,32,33,34,35,36,36,37,38,39,40,41,42,

%U 36,37,38,39,40,41,42,42,43,44,45,46,47,48,48,49,50,51,52,53,54,54,55

%N 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.

%H Seiichi Manyama, <a href="/A303789/b303789.txt">Table of n, a(n) for n = 0..10000</a>

%e 19 = 25_7, so a(19) = 2*6 + 5 = 17.

%e 20 = 26_7, so a(20) = 2*6 + 6 = 18.

%e 21 = 30_7, so a(21) = 3*6 + 0 = 18.

%e 22 = 31_7, so a(22) = 3*6 + 1 = 19.

%o (Ruby)

%o def f(k, ary)

%o   (0..ary.size - 1).inject(0){|s, i| s + ary[i] * k ** i}

%o end

%o def A(k, n)

%o   (0..n).map{|i| f(k, i.to_s(k + 1).split('').map(&:to_i).reverse)}

%o end

%o p A(6, 100)

%o (PARI) a(n) = fromdigits(digits(n, 7), 6); \\ _Michel Marcus_, May 02 2018

%Y 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).

%Y Cf. A037470.

%K nonn,base

%O 0,3

%A _Seiichi Manyama_, Apr 30 2018