A273846 Smallest x > 0 such that 10^x - prime(n) is a prime number or 0 if no such prime exists.

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

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^x-prime(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^x-p), 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