A087606 Smallest k such that n times concatenation of k with itself followed by a 9 is a prime, or 0 if no such number exists.

1, 2, 0, 1, 1, 0, 1, 11, 0, 64, 5, 0, 2, 31, 0, 1, 5, 0, 10, 65, 0, 41, 212, 0, 5, 79, 0, 41, 160, 0, 5, 94, 0, 8, 82, 0, 23, 43, 0, 40, 26, 0, 391, 119, 0, 212, 4, 0, 1, 160, 0, 134, 28, 0, 208, 50, 0, 248, 35, 0, 113, 43, 0, 79, 7, 0, 70, 170, 0, 64, 94, 0, 19, 86, 0, 10, 118, 0, 34, 98

Offset: 1

Author

Amarnath Murthy, Sep 18 2003

Keywords

• base
• nonn

Comments

Conjecture: a(3n) = 0. No other term is zero.

a(3n)=0: consider the sum of the digits modulo 3. For the same reason, if a(m) is divisible by 3 then a(m)=0. - Sam Alexander, Nov 15 2003

Examples

			a(2) = 2 as 229 is a prime. but 119 is not.
		

Links

• XIAO Gang, Factoris - a program that factorizes huge integers, 1997-1999

Crossrefs

Cf. A086920, A087604, A087605, A087607, A087608, A087609, A087610.

Programs

Mathematica

s[b_]:=(v={};l=Length[b];Do[v=Join[v, IntegerDigits[b[[k]]]], {k, l}];v); a[n_]:=If[Mod[n, 3]!= 0, (For[m = 1, ! PrimeQ[10*FromDigits[s[Table[m, {n}]]] +9], m++ ];m), 0]; Table[a[n], {n, 90}] (Firoozbakht)

Extensions

More terms from Sam Alexander, Nov 15 2003

More terms from Farideh Firoozbakht, Feb 04 2005