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A321084
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Primes prime(n) such that 1 + Sum_{k=1..n} 2^(prime(k)-1) is prime.
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OFFSET
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1,1
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COMMENTS
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Primes prime(n) such that A080355(n+1) is prime.
The prime p = 19 gives the prime 332887 = 1010001010001010111_2.
The positions of 1's from the end are 1, 2, 3, 5, 7, 11, 13, 17, 19.
Let S(n) = Sum_{k=1..n} 2^(prime(k)-1). Conjecture: q(n) = 1 + S(n) is prime if and only if 2^S(n) == 1 (mod q(n)).
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LINKS
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EXAMPLE
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a(3) = 5 since 1 + 2^(2-1) + 2^(3-1) + 2^(5-1) = 10111_2 = 23 is prime.
Note that prime(3) = 5 and A080355(3+1) = 23 prime.
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MATHEMATICA
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Prime@ Select[Range[10^3], PrimeQ[1 + Total@ Array[2^(Prime[#] - 1) &, #]] &] (* Michael De Vlieger, Oct 31 2018 *)
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PROG
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(PARI) isok(p) = isprime(p) && isprime(1 + sum(k=1, primepi(p), 2^(prime(k)-1))); \\ Michel Marcus, Oct 27 2018
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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