A346535 Numbers obtained by adding the first k repdigits that consist of the same digit, for some number k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 24, 36, 48, 60, 72, 84, 96, 108, 123, 246, 369, 492, 615, 738, 861, 984, 1107, 1234, 2468, 3702, 4936, 6170, 7404, 8638, 9872, 11106, 12345, 24690, 37035, 49380, 61725, 74070, 86415, 98760, 111105, 123456, 246912, 370368, 493824

Offset: 1

Author

Jwalin Bhatt, Jul 22 2021

Keywords

• nonn
• base
• easy

Examples

			a(1) = 1,
a(2) = 2,
a(3) = 3,
...
a(9) = 9;
a(10) = 1 + 11 = 12,
a(11) = 2 + 22 = 24,
a(12) = 3 + 33 = 36,
...
a(18) = 9 + 99 = 108;
a(19) = 1 + 11 + 111 = 123,
a(20) = 2 + 22 + 222 = 246,
a(21) = 3 + 33 + 333 = 369,
...
a(27) = 9 + 99 + 999 = 1107; ...
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,-21,0,0,0,0,0,0,0,0,10).

Crossrefs

Cf. A010785, A014824.

Programs

Mathematica

Table[m*(10^(1+k)-10-9*k)/81,{k,6},{m,9}]//Flatten (* Stefano Spezia, Aug 17 2021 *)

Python

def sumRepUnits(n): # A014824
  return ((10**n-1)*10 - 9*n)//81
def a(n): # A346535
  d = 1 + (n-1)%9
  m = 1 + (n-1)//9
  return d*sumRepUnits(m)
for n in range(1,1000):
  print(n, a(n))

Formula

a(n) = d*A014824(m) where d = (n-1) mod 9 + 1 and m = ceiling(n/9). - Jon E. Schoenfield, Jul 22 2021

G.f.: x*(1 + 2*x + 3*x^2 + 4*x^3 + 5*x^4 + 6*x^5 + 7*x^6 + 8*x^7 + 9*x^8)/((1 - x^9)^2*(1 - 10*x^9)). - Stefano Spezia, Jul 26 2021