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

Michael De Vlieger, Table of n, a(n) for n = 1..10000

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);

Mathematica

Table[k = 1; p = Prime[n]; While[PrimeQ[10^IntegerLength[k]*p + k], k++]; k, {n, 120}] (* Michael De Vlieger, Jun 30 2025 *)

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: A288739 A111621 A387535 * A078614 A140195 A196564

Adjacent sequences: A326395 A326396 A326397 * A326399 A326400 A326401

Keyword

nonn,base

Author

David James Sycamore, Jun 07 2020

Status

approved