A066065 a(n) = smallest prime q such that in decimal notation the concatenation prime(n)q yields a prime ( = A066064(n)).

3, 7, 3, 3, 3, 7, 3, 3, 3, 3, 3, 3, 11, 3, 23, 23, 3, 3, 3, 29, 3, 7, 11, 23, 7, 3, 3, 11, 3, 11, 7, 47, 3, 13, 3, 31, 31, 7, 29, 3, 11, 19, 3, 3, 3, 3, 3, 7, 3, 3, 3, 3, 7, 11, 17, 3, 3, 3, 7, 11, 3, 11, 13, 23, 7, 23, 3, 3, 29, 13, 3, 3, 3, 3, 3, 3, 17, 19, 3, 3, 11, 7, 17, 7, 7, 71, 3, 37, 41

Offset: 1

Author

Reinhard Zumkeller, Dec 01 2001

Keywords

• base
• nonn

Comments

Conjecture: a(k) < prime(k) for k > 2.

a(n)=3 if and only if prime(n) is in A023238. - Robert Israel, Dec 27 2017

Examples

			A000040(13) = 41; for the first four primes 2, 3, 5 and 7 we get 412, 413, 415 and 417, which are all composite, but with the 5th prime we have 4111 = A066064(13), so a(13) = 11.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..20000 (n=1..1000 from Harry J. Smith)

Crossrefs

Cf. A000040, A023238, A066064.

Programs

Maple

N:= 100: # to get a(1)..a(N)
P:= Vector(N,ithprime):
A:= Vector(N):
q:= 2:
Agenda:= {$1..N}:
while Agenda <> {} do
  q:= nextprime(q);
  m:= 10^(ilog10(q)+1);
  L,Agenda:= selectremove(t -> isprime(P[t]*m+q), Agenda);
  A[convert(L,list)]:= q;
od:
convert(A,list); # Robert Israel, Dec 27 2017

PARI

a(n) = { my(p=prime(n)); forprime(q=3, oo, if(isprime(p*10^(logint(q,10)+1) + q), return(q))) } \\ Harry J. Smith, Nov 09 2009