A176879 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.

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

Offset

1,1

Comments

One of the three primes must be 2. - Robert Israel, Apr 09 2019

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

110=2*5*11; 2^2+5^2+11^2=150+-1 -> primes

Maple

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:
sort([Res]); # Robert Israel, Apr 09 2019

Mathematica

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 *)

Crossrefs

Cf. A006881, A014574, A176875, A176876, A176877, A176878

Sequence in context: A073494 A073488 A244389 * A039447 A345386 A095611

Adjacent sequences: A176876 A176877 A176878 * A176880 A176881 A176882

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Apr 27 2010

Status

approved