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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 (list; graph; refs; listen; history; text; internal format)
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^l-1)*10+7 is divisible by 7 for any l. - Max Alekseyev, Feb 11 2005

LINKS

Table of n, a(n) for n=1..59.

FORMULA

Minimal k such that k*(10^(l*n)-1)/(10^l-1)*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^l-1, 7), for(k=10^(l-1), 10^l-1, if(isprime(k*(10^(l*n)-1)/(10^l-1)*10+7), return(k) ) ) ) ) } (Alekseyev)

CROSSREFS

Cf. A086920, A087604, A087606, A087607, A087608, A087609, A087610.

Sequence in context: A247518 A078076 A010247 * A251636 A248939 A106246

Adjacent sequences:  A087602 A087603 A087604 * A087606 A087607 A087608

KEYWORD

base,nonn

AUTHOR

Amarnath Murthy, Sep 18 2003

EXTENSIONS

Corrected and extended by Max Alekseyev, Feb 11 2005

STATUS

approved

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Last modified June 19 19:49 EDT 2021. Contains 345144 sequences. (Running on oeis4.)