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A084866 Primes that can be written in the form 2*p^2 + 3*q^2 with p and q prime. 5
83, 173, 197, 269, 317, 389, 461, 557, 653, 701, 797, 941, 1091, 1109, 1181, 1229, 1637, 1709, 1949, 1997, 2069, 2141, 2309, 2531, 2549, 2621, 2789, 2861, 3221, 3389, 3461, 3581, 3821, 4157, 4229, 4349, 4493, 5051, 5261, 5381, 5501, 5693 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subsequence of A084864 and of A084865; A084863(a(n))>0.

LINKS

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

EXAMPLE

A000040(40) = 173 = 98 + 75 = 2*7^2 + 3*5^2 = 2*A000040(4)^2 + 3*A000040(3)^2, therefore 173 is a term.

MAPLE

N:= 10^4: # to get terms <= N

P:= select(isprime, [2, seq(i, i=3..floor((N/2)^(1/2)))]):

m:= nops(P):

R:= {}:

for p in P do

  for i from 2 to m while 3*P[i]^2 <= N - 2*p^2 do

    v:= 2*p^2 + 3*P[i]^2;

    if isprime(v) then R:= R union {v} fi

od od:

sort(convert(R, list)); # Robert Israel, Nov 05 2020

MATHEMATICA

nn = 10^4; (* to get terms <= nn *)

P = Select[Join[{2}, Range[3, Floor[Sqrt[nn/2]]]], PrimeQ];

m = Length[P];

R = {};

Do[For[i = 2, 3*P[[i]]^2 <= nn - 2*p^2, i++,

     v = 2*p^2 + 3*P[[i]]^2;

     If[PrimeQ[v], R = R ~Union~ {v}]],

{p, P}];

Sort[R] (* Jean-Fran├žois Alcover, Dec 13 2021, after Robert Israel *)

CROSSREFS

Cf. A084863, A084864, A084865.

Sequence in context: A246874 A136079 A118359 * A142332 A111078 A106962

Adjacent sequences:  A084863 A084864 A084865 * A084867 A084868 A084869

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jun 10 2003

STATUS

approved

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Last modified January 25 19:00 EST 2022. Contains 350572 sequences. (Running on oeis4.)