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

%I A346535 #69 Nov 05 2024 18:59:19
%S A346535 1,2,3,4,5,6,7,8,9,12,24,36,48,60,72,84,96,108,123,246,369,492,615,
%T A346535 738,861,984,1107,1234,2468,3702,4936,6170,7404,8638,9872,11106,12345,
%U A346535 24690,37035,49380,61725,74070,86415,98760,111105,123456,246912,370368,493824
%N A346535 Numbers obtained by adding the first k repdigits that consist of the same digit, for some number k.
%H A346535 <a href="/index/Rec#order_27">Index entries for linear recurrences with constant coefficients</a>, 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).
%F A346535 a(n) = d*A014824(m) where d = (n-1) mod 9 + 1 and m = ceiling(n/9). - _Jon E. Schoenfield_, Jul 22 2021
%F A346535 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
%e A346535 a(1) = 1,
%e A346535 a(2) = 2,
%e A346535 a(3) = 3,
%e A346535 ...
%e A346535 a(9) = 9;
%e A346535 a(10) = 1 + 11 = 12,
%e A346535 a(11) = 2 + 22 = 24,
%e A346535 a(12) = 3 + 33 = 36,
%e A346535 ...
%e A346535 a(18) = 9 + 99 = 108;
%e A346535 a(19) = 1 + 11 + 111 = 123,
%e A346535 a(20) = 2 + 22 + 222 = 246,
%e A346535 a(21) = 3 + 33 + 333 = 369,
%e A346535 ...
%e A346535 a(27) = 9 + 99 + 999 = 1107; ...
%t A346535 Table[m*(10^(1+k)-10-9*k)/81,{k,6},{m,9}]//Flatten (* _Stefano Spezia_, Aug 17 2021 *)
%o A346535 (Python)
%o A346535 def sumRepUnits(n): # A014824
%o A346535   return ((10**n-1)*10 - 9*n)//81
%o A346535 def a(n): # A346535
%o A346535   d = 1 + (n-1)%9
%o A346535   m = 1 + (n-1)//9
%o A346535   return d*sumRepUnits(m)
%o A346535 for n in range(1,1000):
%o A346535   print(n, a(n))
%Y A346535 Cf. A010785, A014824.
%K A346535 nonn,base,easy
%O A346535 1,2
%A A346535 _Jwalin Bhatt_, Jul 22 2021