A096099 a(0) = 1, a(n) = least number such that the concatenation of all terms through a(n) is divisible by prime(n).

1, 2, 3, 5, 5, 2, 13, 25, 8, 22, 16, 26, 35, 35, 11, 26, 48, 58, 6, 46, 4, 77, 83, 29, 33, 187, 61, 78, 81, 23, 183, 15, 22, 68, 8, 137, 84, 178, 99, 7, 71, 82, 142, 241, 133, 71, 56, 19, 32, 318, 157, 199, 303, 16, 201, 201, 213, 257, 355, 229, 365, 379, 345, 27, 52, 19, 272

Offset: 0

Author

Amarnath Murthy, Jun 24 2004

Keywords

• base
• nonn

Comments

Related sequence: numbers k such that a(k) > prime(k): 7, 21, 22, 25, 30, 37, 43, 49, 52, 58, 60, 61, 62 ... (E.g., 7 would be a term since a(7) = 25 > prime(7) = 17.) [edited by Jon E. Schoenfield, Nov 19 2018]

Examples

			a(7) = 25 as the concatenation a(1),a(2),...,a(6),a(7) = 1235521325 == 0 (mod 17), prime(7) = 17.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A073893.

Programs

Mathematica

s = "1"; Print[s]; Do[k = 1; While[Mod[ToExpression[s <> ToString[k]], Prime[n]] != 0, k++ ]; Print[k]; s = s <> ToString[k], {n, 1, 100}] (* Ryan Propper, Sep 03 2005 *)

Extensions

a(10)-a(66) from Ryan Propper, Sep 03 2005