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

1,2

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

Links

Table of n, a(n) for n=1..80.

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

Example

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

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)

Crossrefs

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

Sequence in context: A378068 A216266 A177416 * A382955 A271368 A116799

Adjacent sequences: A087603 A087604 A087605 * A087607 A087608 A087609

Keyword

base,nonn

Author

Amarnath Murthy, Sep 18 2003

Extensions

More terms from Sam Alexander, Nov 15 2003

More terms from Farideh Firoozbakht, Feb 04 2005

Status

approved