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A306920
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a(n) is the smallest prime > 10 where a string of exactly n zeros can be inserted somewhere into the decimal expansion such that the resulting number is also prime.
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5
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11, 19, 17, 13, 13, 23, 17, 17, 31, 13, 23, 41, 137, 61, 23, 13, 13, 67, 53, 89, 19, 107, 17, 29, 61, 263, 31, 37, 127, 53, 269, 199, 137, 23, 31, 89, 61, 13, 43, 163, 53, 131, 109, 19, 79, 283, 109, 19, 269, 223, 97, 97, 223, 89, 13, 79, 67, 107, 17, 389, 197
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OFFSET
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1,1
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COMMENTS
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For many small n, if the decimal expansion of a(n) contains the digit 0, then a(n+1) is a(n) with one zero digit removed. However, this is not true in general. The counterexamples' indices in this sequence are given by A344860.
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LINKS
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EXAMPLE
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For n = 13: If a string of 13 zeros is inserted between the digits 1 and 3 in 137, the resulting number is 1000000000000037, which is prime. Since 137 is the smallest prime where such a string of 13 zeros can be inserted to get another prime, a(13) = 137.
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PROG
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(PARI) insert(n, len, pos) = my(d=digits(n), v=[], w=[]); for(y=1, pos, v=concat(v, d[y])); v=concat(v, vector(len)); for(z=pos+1, #d, v=concat(v, d[z])); subst(Pol(v), x, 10)
a(n) = forprime(p=10, , for(k=1, #digits(p)-1, my(zins=insert(p, n, k)); if(ispseudoprime(zins), return(p))))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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