

A020483


Least prime p such that p+2n is also prime.


28



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

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
If a(n) = a(n+1) = k, then 2*n + k and 2*(n+1) + k are twin primes.  YaPing Lu, Sep 22 2020


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.
Jens Kruse Andersen, Mike Oakes, Ed Pegg Jr, Prime gaps (not necessarily consecutive), digest of 5 messages in primenumbers Yahoo group, Nov 26  Nov 27, 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, A237055.
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

David W. Wilson


EXTENSIONS

a(0)=2 added by N. J. A. Sloane, Apr 25 2015


STATUS

approved



