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A131580
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Least prime P such that P^(2*prime(n))-P^prime(n)-1 is prime with prime(n) the n-th prime.
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1
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2, 3, 2, 3, 163, 19, 151, 263, 131, 3041, 311, 401, 2029, 1163, 2309, 157, 541, 61, 739, 563, 1097, 4813, 1801, 1399, 709, 317, 14563, 863, 5479, 337, 2351, 9533, 4931, 401, 1117, 14639, 17791, 1409, 571, 5171, 16633, 7001, 2129, 10891, 31151, 22709, 6079, 883, 20113
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OFFSET
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1,1
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LINKS
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EXAMPLE
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2^(2*2)-2^2-1=11 prime, 2 is prime, so P = a(1) = 2.
2^(2*3)-2^3-1=55 composite; 3^(2*3)-3^3-1=701 prime, 3 is prime so P = a(2) = 3.
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PROG
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(PARI) a(n) = my(p = prime(n), P=2); while(!isprime(P^(2*p)-P^p-1), P = nextprime(P+1)); P; \\ Michel Marcus, Sep 15 2019
(Magma) sol:=[]; for n in [1..31] do p:=2; while not IsPrime(p^(2*q)-p^ NthPrime(n)-1) where q is NthPrime(n) do p:=NextPrime(p); end while; Append(~sol, p); end for; sol; // Marius A. Burtea, Sep 15 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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