A078294 - OEIS

A078294

Smallest multiple of n in which the most significant occurrence of the digit string of n is preceded and followed by the digit string of (n-1) and (n+1) as can be seen in the forward concatenation of the natural numbers.

%I #5 Dec 05 2013 19:55:57

%S 12,1230,234,3452,4560,5670,6783,7896,8910,910110,101112,1112136,

%T 1213147,1314152,1415160,1516177,16171811,1718190,18192006,19202100,

%U 2021229,2122230,2223249,2324256,25262700,2627289,2728292,28293009

%N Smallest multiple of n in which the most significant occurrence of the digit string of n is preceded and followed by the digit string of (n-1) and (n+1) as can be seen in the forward concatenation of the natural numbers.

%F The following inequality obviously holds for n > 1: a(n) >= (n-1)*10^(floor(1+log n) + floor(1+log(n+1))) + n*10^(floor(1+log(n+1))) + n + 1 where log is taken base 10, not base e. - _Sam Alexander_, Oct 19 2003

%e a(1) = 12 = 012, a(9) = 8910, a(13) = 1213147, 13 is sandwiched between 12 and 14.

%K base,nonn

%O 1,1

%A _Amarnath Murthy_, Nov 26 2002

%E Corrected and extended by _Sam Alexander_, Oct 19 2003