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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 18 08:45 EDT 2024. Contains 375999 sequences. (Running on oeis4.)