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%I #57 Jul 06 2020 20:16:23
%S 1,2,1,2,1,2,1,2,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,1,1,1,1,1,
%T 1,2,2,1,1,1,1,2,1,2,1,1,2,1,1,1,1,1,2,1,1,1,1,2,1,1,1,1,1,1,1,1,1,2,
%U 1,2,1,1,2,1,1
%N a(n) is the smallest k > 0 such that the concatenation prime(n)k is composite.
%C a(n) can only be 1 or 2 for any n >= 1. It appears that there are many more primes for which k = 1 than those for which k = 2 (~ 91% of the first 10^7 primes have k = 1).
%F a(n) = 2 if prime(n) is in A023237, else a(n) = 1. [corrected by _Chai Wah Wu_, Jul 06 2020]
%e a(1) = 1 because 21 is prime, a(2) = 2 because 31 is prime (as 3 is in A023237), and 32 is composite
%p P := proc (n)
%p if isprime(10*ithprime(n)+1) then return 2 else 1;
%p end if:
%p end proc;
%p P(50);
%p seq(P(k), k = 1 .. 50);
%o (PARI) a(n) = my(k=1, p=Str(prime(n))); while (isprime(eval(concat(p, Str(k)))), k++); k; \\ _Michel Marcus_, Jun 07 2020
%Y Cf. A000040, A023237.
%K nonn,base
%O 1,2
%A _David James Sycamore_, Jun 07 2020
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