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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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

CROSSREFS

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

Sequence in context: A073494 A073488 A244389 * A039447 A095611 A307534

Adjacent sequences:  A176876 A176877 A176878 * A176880 A176881 A176882

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Apr 27 2010

STATUS

approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)