

A087605


Smallest k such that n times concatenation of k with itself followed by a 7 is a prime, or 0 if no such number exists.


7



1, 2, 1, 1, 3, 100005, 1, 2, 4, 6, 8, 100010, 19, 2, 215, 9, 60, 100041, 4, 66, 5, 1, 41, 100061, 4, 15, 2, 1, 195, 100055, 61, 1061, 143, 12, 72, 100127, 19, 60, 1, 6, 125, 0, 45, 1305, 3, 39, 27, 100269, 72, 95, 136, 1123, 50, 100193, 52, 1056, 176, 1536, 66
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OFFSET

1,2


COMMENTS

a(42n)=0, but all other terms are probably nonzero. For n a multiple of 42, (10^(l*n)1)/(10^l1)*10+7 is divisible by 7 for any l.  Max Alekseyev, Feb 11 2005


LINKS



FORMULA

Minimal k such that k*(10^(l*n)1)/(10^l1)*10+7 is prime, where l is the length of k; and 0 if no such prime exists.  Max Alekseyev, Feb 11 2005


EXAMPLE

a(5) = 3 as 333337 is a prime but 111117 and 222227 are not.


PROG

(PARI) { a(n) = if(n%42==0, return(0)); for(l=1, 10^6, if(valuation(10^(l*n)1, 7)==valuation(10^l1, 7), for(k=10^(l1), 10^l1, if(isprime(k*(10^(l*n)1)/(10^l1)*10+7), return(k) ) ) ) ) } (Alekseyev)


CROSSREFS



KEYWORD

base,nonn


AUTHOR



EXTENSIONS



STATUS

approved



