

A273846


Smallest x > 0 such that 10^x  prime(n) is a prime number or 0 if no such prime exists.


1



0, 1, 0, 0, 2, 0, 2, 0, 3, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 12, 0, 9, 0, 3, 0, 22, 3, 0, 4, 0, 0, 0, 4, 3, 3, 0, 3, 0, 4, 0, 0, 0, 3, 0, 4, 3, 0, 4, 3, 18, 11, 0, 0, 3, 0, 5, 0, 4, 0, 3, 0, 0, 3, 0, 3, 3, 0, 0, 0, 3, 5, 0, 3, 0, 5, 0, 3, 0
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OFFSET

1,5


COMMENTS

For p(1) = 2, 10^x  2 is divisible by 2 for all x > 0 so a(1) = 0.
For p(3) = 5, 10^x  5 is divisible by 5 for all x > 0 so a(3) = 0.
For all prime(i) of the form 3*k+1, 10^xprime(i) is divisible by 3 so a(i) = 0.
For n = 913, prime(n) = 7127, if x exists then x > 16000.


LINKS

Pierre CAMI, Table of n, a(n) for n = 1..912


EXAMPLE

10^1  3 = 7 is prime, so a(2) = 1 as 3 = prime(2).
10^1  11 is composite, 10^2  11 = 89 is prime, so a(5) = 2 as 11 = prime(5).


PROG

(PARI) a(n) = if((p=prime(n))%3==1  n==1  n==3, 0, for(x=1, oo, if(ispseudoprime(10^xp), return(x)))); \\ Jinyuan Wang, Mar 05 2020


CROSSREFS

Sequence in context: A029188 A317844 A318447 * A090290 A153585 A169611
Adjacent sequences: A273843 A273844 A273845 * A273847 A273848 A273849


KEYWORD

nonn


AUTHOR

Pierre CAMI, Jun 01 2016


STATUS

approved



