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

1,1

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

Links

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

Example

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.

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

Prog

(PARI) digitsIn(x)= { local(d); if (x==0, return(1)); d=1 + log(x)\log(10); if (10^d == x, d++, if (10^(d-1) > x, d--)); return(d) }
Concat(a, b)= { return(a*10^digitsIn(b) + b) }
{ for (n = 1, 1000, p=prime(n); q=2; while(!isprime(Concat(p, q)), q=nextprime(q + 1)); write("b066065.txt", n, " ", q) ) } \\ Harry J. Smith, Nov 09 2009

Crossrefs

Cf. A000040, A023238, A066064.

Sequence in context: A019973 A010623 A283245 * A145511 A242461 A065443

Adjacent sequences: A066062 A066063 A066064 * A066066 A066067 A066068

Keyword

base,nonn

Author

Reinhard Zumkeller, Dec 01 2001

Status

approved