A237055 -id:A237055 - cp's OEIS frontend

A020483 Least prime p such that p+2n is also prime.

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

Offset: 0

David W. Wilson

nonn

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

			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.

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.

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

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

a020483 n = head [p | p <- a000040_list, a010051' (p + 2 * n) == 1]
-- Reinhard Zumkeller, Nov 29 2014

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

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 *)

a(n)=forprime(p=2,,if(isprime(p+2*n), return(p))) \\ Charles R Greathouse IV, Mar 19 2014

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

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

A108184 a(n) = smallest prime such that a(n) + 2n is also prime and such that a(n) > a(n-1).

Original entry on oeis.org

2, 3, 7, 11, 23, 31, 41, 47, 67, 71, 83, 109, 113, 131, 139, 149, 167, 193, 197, 233, 241, 251, 263, 271, 283, 317, 331, 347, 353, 373, 379, 401, 439, 443, 479, 487, 491, 503, 523, 541, 563, 571, 577, 587, 613, 619, 641, 727, 733, 761, 787, 809, 863, 877

Offset: 0

Giovanni Teofilatto, Jun 28 2005

Increasing primes p such that p + 2n is prime.

			a(0)=2 since 2+0=2 is prime; a(1)=3 since 3+2=5 is prime.
a(2)=7 since 7+4=11 is prime; 5 is not in the sequence since 5+4=9 is not prime.

T. D. Noe, Table of n, a(n) for n = 0..10000

Cf. A020483, A237055

A108184 := proc(n) option remember; if n = 1 then 3; else for a from procname(n-1)+1 do if isprime(a) and isprime(a+2*n) then RETURN(a) ; fi; od: fi; end: seq(A108184(n),n=1..100) ; # R. J. Mathar, Jan 31 2009

t = {2}; Do[p = NextPrime[t[[-1]]]; While[! PrimeQ[p + 2 n], p = NextPrime[p]]; AppendTo[t, p], {n, 100}]; t (* T. D. Noe, Feb 04 2014 *)

A108184(maxp) = {my(a=[2], n=1); forprime(p=3, maxp, if(isprime(p+2*n), n++; a=concat(a, p))); a} \\ Colin Barker, Feb 03 2014

Edited and extended by Ray Chandler, Jul 07 2005

Edited by N. J. A. Sloane, Feb 11 2009 at the suggestion of R. J. Mathar

cp's OEIS Frontend

A020483 Least prime p such that p+2n is also prime.

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