

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 (n1) and (n+1) as can be seen in the forward concatenation of the natural numbers.


0



12, 1230, 234, 3452, 4560, 5670, 6783, 7896, 8910, 910110, 101112, 1112136, 1213147, 1314152, 1415160, 1516177, 16171811, 1718190, 18192006, 19202100, 2021229, 2122230, 2223249, 2324256, 25262700, 2627289, 2728292, 28293009
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..28.


FORMULA

The following inequality obviously holds for n > 1: a(n) >= (n1)*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


EXAMPLE

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


CROSSREFS

Sequence in context: A301474 A054351 A080814 * A317953 A009155 A078296
Adjacent sequences: A078291 A078292 A078293 * A078295 A078296 A078297


KEYWORD

base,nonn


AUTHOR

Amarnath Murthy, Nov 26 2002


EXTENSIONS

Corrected and extended by Sam Alexander, Oct 19 2003


STATUS

approved



