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A020483
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Least prime p such that p+2n is also prime.
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29
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2, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 7, 5, 3, 3, 7, 5, 3, 5, 3, 3, 5, 3, 7, 5, 3, 7, 5, 3, 3, 7, 5, 3, 5, 3, 3, 7, 5, 3, 5, 3, 7, 5, 3, 13, 7, 5, 3, 5, 3, 3, 5, 3, 3, 5, 3, 19, 13, 11, 13, 7, 5, 3, 5, 3, 7, 5, 3, 3, 11, 11, 7, 5, 3, 3, 7, 5, 3, 7, 5, 3, 5, 3, 7, 5, 3, 7, 5, 3, 3, 11, 11, 7, 5, 3, 3, 5, 3, 3, 13, 11, 31, 7
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OFFSET
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0,1
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COMMENTS
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It is conjectured that a(n) always exists. a(n) has been computed for n < 5 * 10^11, with largest value a(248281210271) = 3307. - Jens Kruse Andersen, Nov 28 2004
If a(n) = a(n+1) = k, then 2*n + k and 2*(n+1) + k are twin primes. - Ya-Ping Lu, Sep 22 2020
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LINKS
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FORMULA
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If a(n) exists, a(n) < 2n, which of course is a great overestimate. - T. D. Noe, Jul 16 2002
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EXAMPLE
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Given n = 2, we see that 2 + 2n = 6 = 2 * 3, but 3 + 2n = 7, which is prime, so a(2) = 3.
Given n = 3, we see that 2 + 2n = 8 = 2^3 and 3 + 2n = 9 = 3^2, but 5 + 2n = 11, which is prime, so a(3) = 5.
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MAPLE
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local p;
p := 2;
while true do
if isprime(p+2*n) then
return p;
end if;
p := nextprime(p) ;
end do:
end proc:
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MATHEMATICA
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Table[j = 1; found = False; While[!found, j++; found = PrimeQ[Prime[j] + 2i]]; Prime[j], {i, 200}]
leastPrimep2n[n_] := Block[{k = 1, p, q = 2 n}, While[p = Prime@k; !PrimeQ[p + q], k++]; p]; Array[leastPrimep2n, 102] (* Robert G. Wilson v, Mar 26 2008 *)
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PROG
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(Haskell)
a020483 n = head [p | p <- a000040_list, a010051' (p + 2 * n) == 1]
(GAP) P:=Filtered([1..10000], IsPrime);;
a:=List(List([0..110], n->Filtered(P, i->IsPrime(i+2*n))), Minimum); # Muniru A Asiru, Mar 26 2018
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CROSSREFS
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It is likely that A054906 is an identical sequence, although this seems to have not yet been proved. - N. J. A. Sloane, Feb 06 2017
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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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