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A176879
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Numbers that are the product of 3 distinct primes a,b and c, such that a^2+b^2+c^2 is the average of a twin prime pair.
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2
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110, 130, 430, 442, 470, 670, 782, 790, 890, 970, 1222, 1310, 1358, 1462, 1582, 1670, 1898, 1978, 2338, 2410, 2510, 3082, 3170, 3478, 3970, 4090, 4430, 4718, 4982, 5402, 5410, 5542, 5678, 6298, 7390, 7582, 7918, 7922, 8570, 8878, 9062, 9178, 9682, 9698
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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110=2*5*11; 2^2+5^2+11^2=150+-1 -> primes
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MAPLE
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N:= 10000: # to get terms <= N
P:= select(isprime, [seq(i, i=5..N/10, 2)]): nP:= nops(P):
Res:= NULL:
for i from 1 to nP do
a:= P[i];
for j from i+1 to nP do
b:= P[j];
if 2*a*b > N then break fi;
q:= 4+a^2 + b^2;
if isprime(q-1) and isprime(q+1) then Res:= Res, 2*a*b; fi;
od
od:
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MATHEMATICA
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l[n_]:=Last/@FactorInteger[n]; f[n_]:=First/@FactorInteger[n]; lst={}; Do[If[l[n]=={1, 1, 1}, a=f[n][[1]]; b=f[n][[2]]; c=f[n][[3]]; If[PrimeQ[a^2+b^2+c^2-1]&&PrimeQ[a^2+b^2+c^2+1], AppendTo[lst, n]]], {n, 8!}]; lst
With[{nn=2000}, Select[Union[2Times@@#&/@Select[Subsets[Prime[Range[2, nn]], {2}], AllTrue[Total[#^2]+4+{1, -1}, PrimeQ]&]], #<=6nn&]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 20 2020 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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