A326398 a(n) is the smallest k > 0 such that the concatenation prime(n)k is composite.

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, 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, 1, 2, 1, 1, 2, 1, 1

Offset

1,2

Comments

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).

Links

Table of n, a(n) for n=1..75.

Formula

a(n) = 2 if prime(n) is in A023237, else a(n) = 1. [corrected by Chai Wah Wu, Jul 06 2020]

Example

a(1) = 1 because 21 is prime, a(2) = 2 because 31 is prime (as 3 is in A023237), and 32 is composite

Maple

P := proc (n)
if isprime(10*ithprime(n)+1) then return 2 else 1;
end if:
end proc;
P(50);
seq(P(k), k = 1 .. 50);

Prog

(PARI) a(n) = my(k=1, p=Str(prime(n))); while (isprime(eval(concat(p, Str(k)))), k++); k; \\ Michel Marcus, Jun 07 2020

Crossrefs

Cf. A000040, A023237.

Sequence in context: A319610 A288739 A111621 * A140195 A196564 A196563

Adjacent sequences: A326395 A326396 A326397 * A326399 A326400 A326401

Keyword

nonn,base

Author

David James Sycamore, Jun 07 2020

Status

approved