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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. 5
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 (list; graph; refs; listen; history; text; internal format)
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: A097435 A073954 A227868 * A257767 A158136 A153874

Adjacent sequences:  A176873 A176874 A176875 * A176877 A176878 A176879

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Apr 27 2010

STATUS

approved

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Last modified November 11 18:50 EST 2019. Contains 329031 sequences. (Running on oeis4.)