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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 20 03:20 EDT 2021. Contains 345157 sequences. (Running on oeis4.)