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

1,2

Links

Table of n, a(n) for n=1..49.

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).

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

Example

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; ...

Mathematica

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

Prog

(Python 3)
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))

Crossrefs

Cf. A010785, A014824.

Sequence in context: A259236 A138141 A228017 * A227224 A236750 A001102

Adjacent sequences: A346532 A346533 A346534 * A346536 A346537 A346538

Keyword

nonn,base,easy

Author

Jwalin Bhatt, Jul 22 2021

Status

approved