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A087711
a(n) = smallest number k such that both k-n and k+n are primes.
10
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
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. A082467. See A137169 for another version.
Cf. A020483.
Sequence in context: A330434 A330424 A057168 * A123128 A057064 A340781
KEYWORD
easy,nonn
AUTHOR
Zak Seidov, Sep 28 2003
EXTENSIONS
Entries checked by Klaus Brockhaus, Apr 08 2007
STATUS
approved