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A334287
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Smallest full reptend prime p such that there is a gap of exactly 2n between p and the next full reptend prime, or 0 if no such prime exists.
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1
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17, 19, 23, 491, 7, 47, 419, 577, 29, 0, 1789, 233, 461, 433, 193, 509, 823, 61, 1979, 1327, 659, 269, 11503, 1381, 887, 14251, 3167, 8297, 3469, 0, 7247, 15073, 2473, 743, 19309, 4349, 21503, 12823, 14939, 3863, 5419, 6389, 24137, 27211, 10343, 13577, 18979
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OFFSET
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1,1
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COMMENTS
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Gaps of length congruent to 20 mod 40 do not exist. All full reptend primes are either 7, 11, 17, 19, 21, 23, 29, or 33 mod 40, and no difference of 20 exists between any of these numbers.
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LINKS
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Martin Raab, Table of n, a(n) for n = 1..583
Eric Weisstein's World of Mathematics, Full Reptend Prime
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EXAMPLE
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a(9) = 29 because there is a gap of 2*9 = 18 between 29 and the next full reptend prime 47.
a(10) = 0 because no gap of 2*10 = 20 exists between full reptend primes.
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PROG
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(PARI) is(p) = Mod(10, p)^(p\2)==-1 && znorder(Mod(10, p))+1==p;
isok(p, n) = {if (! is(p), return (0)); if (isprime(p+n) && is(p+n), forprime(q=p+1, p+n-1, if (is(q), return (0)); ); return (1); ); }
a(n) = {n *= 2; if ((n % 40) == 20, return (0)); my (p = 2); while (! isok(p, n), p = nextprime(p+1)); p; } \\ Michel Marcus, Apr 22 2020
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CROSSREFS
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Cf. A001913.
Sequence in context: A288613 A154881 A226684 * A249566 A205646 A281192
Adjacent sequences: A334284 A334285 A334286 * A334288 A334289 A334290
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KEYWORD
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nonn
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AUTHOR
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Martin Raab, Apr 21 2020
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STATUS
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approved
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