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 A020483 Least prime p such that p+2n is also prime. 27
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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 LINKS T. D. Noe, Table of n, a(n) for n = 0..10000 Jens Kruse Andersen, Prime gaps (not necessarily consecutive), Yahoo! group "primenumbers", Nov 26 2004. FORMULA If a(n) exists, a(n) < 2n, which of course is a great overestimate. - T. D. Noe, Jul 16 2002 a(n) = A087711(n) - n. - Zak Seidov, Nov 28 2007 a(n) = A020484(n) - 2n. - Zak Seidov, May 29 2014 a(n) = 2 if and only if n = 0. - Alonso del Arte, Mar 14 2018 EXAMPLE 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. MAPLE A020483 := proc(n)     local p;     p := 2;     while true do         if isprime(p+2*n) then             return p;         end if;         p := nextprime(p) ;     end do: end proc: seq(A020483(n), n=0..40); # R. J. Mathar, Sep 23 2016 MATHEMATICA 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 *) PROG (PARI) a(n)=forprime(p=2, , if(isprime(p+2*n), return(p))) \\ Charles R Greathouse IV, Mar 19 2014 (Haskell) a020483 n = head [p | p <- a000040_list, a010051' (p + 2 * n) == 1] -- Reinhard Zumkeller, Nov 29 2014 (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 CROSSREFS Cf. A087711, A101042, A101043, A101044, A101045, A101046. Cf. A101045, A239392 (record values). Cf. A000040, A010051, A020484. 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 Sequence in context: A063256 A229703 A131320 * A119912 A076368 A279931 Adjacent sequences:  A020480 A020481 A020482 * A020484 A020485 A020486 KEYWORD nonn AUTHOR EXTENSIONS a(0)=2 added by N. J. A. Sloane, Apr 25 2015 STATUS approved

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Last modified October 17 22:28 EDT 2019. Contains 328134 sequences. (Running on oeis4.)