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A326398 a(n) is the smallest k > 0 such that the concatenation prime(n)k is composite. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 2 06:52 EDT 2021. Contains 346411 sequences. (Running on oeis4.)