A087711 a(n) = smallest number k such that both k-n and k+n are primes.

2, 4, 5, 8, 7, 8, 11, 10, 11, 14, 13, 18, 17, 16, 17, 22, 21, 20, 23, 22, 23, 26, 25, 30, 29, 28, 33, 32, 31, 32, 37, 36, 35, 38, 37, 38, 43, 42, 41, 44, 43, 48, 47, 46, 57, 52, 51, 50, 53, 52, 53, 56, 55, 56, 59, 58, 75, 70, 69, 72, 67, 66, 65, 68, 67, 72, 71, 70, 71, 80, 81, 78

Offset

0,1

Comments

Let b(n), c(n) and d(n) be respectively, smallest number m such that phi(m-n) + sigma(m+n) = 2n, smallest number m such that phi(m+n) + sigma(m-n) = 2n and smallest number m such that phi(m-n) + sigma(m+n) = phi(m+n) + sigma(m-n), we conjecture that for each positive integer n, a(n)=b(n)=c(n)=d(n). Namely we conjecture that for each positive integer n, a(n) < A244446(n), a(n) < A244447(n) and a(n) < A244448(n). - Jahangeer Kholdi and Farideh Firoozbakht, Sep 05 2014

Links

Zak Seidov, Table of n, a(n) for n = 0..1000

Formula

a(n) = A020483(n)+n for n >= 1. - Robert Israel, Sep 08 2014

Example

n=10: k=13 because 13-10 and 13+10 are both prime and 13 is the smallest k such that k +/- 10 are both prime
4-1=3, prime, 4+1=5, prime; 5-2=3, 5+2=7; 8-3=5, 8+3=11; 9-4=5, 9+4=13, ...

Maple

Primes:= select(isprime, {seq(2*i+1, i=1..10^3)}):
a[0]:= 2:
for n from 1 do
  Q:= Primes intersect map(t -> t-2*n, Primes);
  if nops(Q) = 0 then break fi;
  a[n]:= min(Q) + n;
od:
seq(a[i], i=0..n-1); # Robert Israel, Sep 08 2014

Mathematica

s = ""; k = 0; For[i = 3, i < 22^2, If[PrimeQ[i - k] && PrimeQ[i + k], s = s <> ToString[i] <> ", "; k++ ]; i++ ]; Print[s] (* Vladimir Joseph Stephan Orlovsky, Apr 03 2008 *)
snk[n_]:=Module[{k=n+1}, While[!PrimeQ[k+n]||!PrimeQ[k-n], k++]; k]; Array[ snk, 80, 0] (* Harvey P. Dale, Dec 13 2020 *)

Prog

(Magma) distance:=function(n); k:=n+2; while not IsPrime(k-n) or not IsPrime(k+n) do k:=k+1; end while; return k; end function; [ distance(n): n in [1..71] ]; /* Klaus Brockhaus, Apr 08 2007 */
(PARI) a(n)=my(k); while(!isprime(k-n) || !isprime(k+n), k++); return(k) \\ Edward Jiang, Sep 05 2014

Crossrefs

Cf. A087695, A087696, A087697, A087678, A087679, A087680, A087681, A087682, A087683.

Cf. A082467. See A137169 for another version.

Cf. A244446, A244447, A244448.

Cf. A020483.

Sequence in context: A330434 A330424 A057168 * A123128 A057064 A340781

Adjacent sequences: A087708 A087709 A087710 * A087712 A087713 A087714

Keyword

easy,nonn

Author

Zak Seidov, Sep 28 2003

Extensions

Entries checked by Klaus Brockhaus, Apr 08 2007

Status

approved