A075000 Smallest number such that n*a(n) is a concatenation of n consecutive integers; or 0 if no such number exists.

1, 6, 41, 864, 2469, 20576, 493827, 7098637639, 13717421, 1234567891, 82737383012865106529, 10288065758426, 3513762316247164732, 563643651522439401227280, 8230452606740808761

Offset: 1

Author

Amarnath Murthy, Aug 31 2002

Keywords

• base
• nonn

Comments

Conjecture: For every n there exists a nonzero a(n).

Examples

			a(11) = 82737383012865106529 as 11*82737383012865106529 = 910111213141516171819 is the concatenation of 11 numbers from 9 to 19.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A074991, A074992, A074993, A074994, A074995, A074996, A036377, A073086, A074999, A075001.

Programs

Mathematica

f[ n_ ] := Block[ {id = Range@n}, While[ k = FromDigits@ Flatten@ IntegerDigits@ id/n; !IntegerQ@k, id++ ]; k ]; Array[ f, 16 ] (* Robert G. Wilson v, Oct 19 2007 *)

Formula

a(n) = A077306(n)/n. - Amarnath Murthy, Nov 03 2002

Extensions

More terms from Rick L. Shepherd, Sep 03 2002