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.

12, 1230, 234, 3452, 4560, 5670, 6783, 7896, 8910, 910110, 101112, 1112136, 1213147, 1314152, 1415160, 1516176, 16171811, 1718190, 18192006, 19202100, 2021229, 2122230, 2223249, 2324256, 24252600, 25262718, 2627289, 2728292, 28293009, 2930310, 30313226

Offset

1,1

Links

Table of n, a(n) for n=1..31.

Formula

The following inequality obviously holds for n > 1: a(n) >= (n-1)*10^(floor(1+log10(n)) + floor(1+log10(n+1))) + n*10^(floor(1+log10(n+1))) + n + 1. - 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: A054351 A080814 A340834 * 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

a(16) and a(26) corrected, missing a(25) inserted, and more terms from Sean A. Irvine, Jun 26 2025

Status

approved