A176876 Numbers that are the product of two distinct primes a and b, such that a^3+b^3 is the average of a twin prime pair.

143, 215, 341, 485, 515, 551, 713, 1133, 1241, 1271, 1541, 1865, 2183, 2315, 2501, 3173, 3215, 3503, 3713, 4031, 4661, 5465, 5633, 6431, 6485, 7313, 7361, 7571, 8201, 8471, 9353, 9599, 9713, 9893, 12083, 12371, 12443, 12449, 13361, 13631, 14711

Offset

1,1

Comments

All terms == 5 (mod 6). - Robert Israel, Apr 09 2019

Links

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

Example

143=11*13; 11^3+13^3=3528+-1 -> primes,...

Maple

N:= 20000: # to get all terms <= N
P1:= select(isprime, [seq(i, i=7..N/5, 6)]):n1:= nops(P1):
P2:= select(isprime, [seq(i, i=5..N/7, 6)]):n2:= nops(P2):
Res:= NULL:
for i from 1 to n1 do
  a:= P1[i];
  for j from 1 to n2 do
    b:= P2[j];
    if a*b > N then break fi;
    q:= a^3 + b^3;
    if isprime(q-1) and isprime(q+1) then Res:= Res, 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}, a=f[n][[1]]; b=f[n][[2]]; If[PrimeQ[a^3+b^3-1]&&PrimeQ[a^3+b^3+1], AppendTo[lst, n]]], {n, 8!}]; lst

Crossrefs

Cf. A006881, A014574, A176875

Sequence in context: A073954 A227868 A353059 * A257767 A158136 A153874

Adjacent sequences: A176873 A176874 A176875 * A176877 A176878 A176879

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Apr 27 2010

Status

approved