A077183 Smallest number k such that the reverse concatenation of natural numbers from k to 1 is divisible by prime(n), or 0 if no such number exists.

0, 2, 0, 2, 14, 15, 9, 5, 16, 4, 25, 21, 40, 67, 78, 66, 25, 111, 161, 49, 30, 15, 27, 20, 63, 98, 102, 3, 99, 92, 296, 71, 22, 367, 4, 48, 50, 91, 45, 241, 137, 258, 23, 28, 212, 40, 96, 408, 456, 110, 16, 731, 403, 667, 90, 130, 111, 458, 146, 18, 577, 276, 708

Offset

1,2

Comments

Conjecture: a(n) > 0 for all n > 3, since prime(1) = 2 and prime(3) = 5 are the only primes whose multiples cannot end in 1. - Ryan Propper, Jul 29 2005

Links

Daniel Mondot, Table of n, a(n) for n = 1..1000

Ralf Stephan, Factors and Primes in Two Smarandache Sequences, Smar. Notions 9 (1998), pp. 4-10.

Example

a(4) = 2 as 21 is divisible by prime(4) = 7.
The smallest reverse concatenation of natural numbers k..1 that is divisible by prime(5) = 11 is 1413121110987654321, so a(5) = k = 14.

Mathematica

Do[p = Prime[n]; k = 1; s = ToString[k]; While[Mod[ToExpression[s], p] > 0, k++; s = ToString[k] <> s]; Print[k], {n, 4, 50}] (* Ryan Propper, Jul 29 2005 *)

Crossrefs

Cf. A077180, A077181, A077182, A077185.

Sequence in context: A281205 A285152 A077184 * A101030 A093857 A056949

Adjacent sequences: A077180 A077181 A077182 * A077184 A077185 A077186

Keyword

base,nonn

Author

Amarnath Murthy, Nov 01 2002

Extensions

Corrected and extended by Ralf Stephan, Mar 18 2003

Example clarified by Harvey P. Dale, Aug 22 2013

Status

approved