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%I #16 Dec 28 2017 03:37:02
%S 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,
%T 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,
%U 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
%N a(n) = smallest prime q such that in decimal notation the concatenation prime(n)q yields a prime ( = A066064(n)).
%C Conjecture: a(k) < prime(k) for k > 2.
%C a(n)=3 if and only if prime(n) is in A023238. - _Robert Israel_, Dec 27 2017
%H Robert Israel, <a href="/A066065/b066065.txt">Table of n, a(n) for n = 1..20000</a> (n=1..1000 from Harry J. Smith)
%e 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.
%p N:= 100: # to get a(1)..a(N)
%p P:= Vector(N,ithprime):
%p A:= Vector(N):
%p q:= 2:
%p Agenda:= {$1..N}:
%p while Agenda <> {} do
%p q:= nextprime(q);
%p m:= 10^(ilog10(q)+1);
%p L,Agenda:= selectremove(t -> isprime(P[t]*m+q), Agenda);
%p A[convert(L,list)]:= q;
%p od:
%p convert(A,list); # _Robert Israel_, Dec 27 2017
%o (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) }
%o Concat(a, b)= { return(a*10^digitsIn(b) + b) }
%o { 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
%Y Cf. A000040, A023238, A066064.
%K base,nonn
%O 1,1
%A _Reinhard Zumkeller_, Dec 01 2001
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