A267327 - OEIS

%I #32 Jan 18 2016 16:50:37

%S 1,112,2223,33334,444445,5555556,66666667,777777778,8888888889,

%T 999999999910,101010101010101010101011,11111111111111111111111112,

%U 1212121212121212121212121213,131313131313131313131313131314,14141414141414141414141414141415,1515151515151515151515151515151516

%N a(n) = decimal expansion of (n-1) prepended n times to the decimal expansion of n (n > 0).

%C These terms are primes: a(7), a(19), a(989), a(1187), a(4183); see A267237.

%F a(n) = (10^(n+1)*(n-1) - n + 10) / 9 (n <= 9).

%F a(n) = Sum_{i=0...n+1} (n*10^(i*(floor(log(10, n+1)) + 1))) + 1  (n <> 10^k, k > 0), i.e. doesn't give correctly the terms ending with 0.

%e a(3) = 2223 ('3-1' prepended 3 times to '3').

%t Table[ FromDigits[ StringJoin@@ ToString/@ PadLeft[{n}, n+1, n-1]], {n, 50}](* Or *)

%t FromDigits/@ Table[ Nest[ ToString[n] <> #&, ToString[n+1], n+1], {n, 0, 50}]

%Y Cf. A000461, A158849, A158859, A267237.

%K nonn,easy,base

%O 1,2

%A _Mikk Heidemaa_, Jan 13 2016