A358986 - OEIS

%I #14 Dec 09 2022 10:53:32

%S 10,28,207,548,3966,10462,75435,198890,1433489,3779246

%N a(n) is the number of numbers of the form k + reverse(k) for at least one number k < 10^n.

%C This sequence differs from the partial sums of A358985; see the Example section.

%e There are 10 numbers of the form k + reverse(k) for 1-digit numbers k -- 0, 2, 4, 6, 8, 10, 12, 14, 16, and 18 -- so a(1) = 10.

%e There are 18 numbers of the form k + reverse(k) for 2-digit numbers k -- 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, and 198 -- and none of these 18 numbers are among the 10 numbers counted in a(1), so a(2) = 10 + 18 = 28.

%e There are 180 numbers of the form k + reverse(k) for 3-digit numbers k, but exactly one of those -- 121 = 110 + reverse(110) = 110 + 11 -- is also a number of the form k + reverse(k) for a 2-digit number k: e.g., 29 + reverse(29) = 29 + 92 = 121. So a(3) = 10 + 18 + 180 - 1 = 207.

%o (Python)

%o def A358986(n):

%o     kset = set()

%o     for i in range(1,10**(n-1)):

%o         for j in range(int((s:=str(i))[0])+1):

%o             kset.add(10*i+j+int(str(j)+s[::-1]))

%o     return 10+len(kset) # _Chai Wah Wu_, Dec 09 2022

%Y Cf. A067030, A358985.

%K nonn,base,more

%O 1,1

%A _Jon E. Schoenfield_, Dec 08 2022

%E a(8)-a(10) from _Chai Wah Wu_, Dec 09 2022