A267327 - OEIS

A267327

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

1, 112, 2223, 33334, 444445, 5555556, 66666667, 777777778, 8888888889, 999999999910, 101010101010101010101011, 11111111111111111111111112, 1212121212121212121212121213, 131313131313131313131313131314, 14141414141414141414141414141415, 1515151515151515151515151515151516

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OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..16.

FORMULA

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

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.

EXAMPLE

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