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A087711
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a(n) = smallest number k such that both k-n and k+n are primes.
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10
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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
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OFFSET
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0,1
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COMMENTS
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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
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LINKS
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FORMULA
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EXAMPLE
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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, ...
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MAPLE
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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:
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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