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A346535
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Numbers obtained by adding the first k repdigits that consist of the same digit, for some number k.
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2
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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
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OFFSET
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1,2
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LINKS
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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).
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FORMULA
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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
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EXAMPLE
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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; ...
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MATHEMATICA
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Table[m*(10^(1+k)-10-9*k)/81, {k, 6}, {m, 9}]//Flatten (* Stefano Spezia, Aug 17 2021 *)
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PROG
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(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))
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CROSSREFS
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Cf. A010785, A014824.
Sequence in context: A259236 A138141 A228017 * A227224 A236750 A001102
Adjacent sequences: A346532 A346533 A346534 * A346536 A346537 A346538
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KEYWORD
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nonn,base,easy
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AUTHOR
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Jwalin Bhatt, Jul 22 2021
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STATUS
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approved
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