A103558 Semiprimes of the form p^2 + q^2, where p and q are primes.

34, 58, 74, 146, 178, 194, 218, 298, 314, 365, 386, 458, 482, 533, 538, 554, 698, 818, 866, 965, 1082, 1202, 1322, 1418, 1538, 1658, 1685, 1706, 1853, 1858, 1874, 2018, 2042, 2138, 2218, 2234, 2258, 2498, 2642, 2813, 2818, 2858, 2978, 3098, 3218, 3338

Offset

1,1

Comments

p and q must be distinct, otherwise p^2 + q^2 = 2*p*p has three prime factors. - Klaus Brockhaus

Even terms are 2*A103739. - Robert Israel, Nov 03 2017

Links

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

Example

34 is a term because 3^2 + 5^2 = 34 = 2*17; 58 is a term because 3^2 + 7^2 = 58 = 2*29; 74 is a term because 5^2 + 7^2 = 74 = 2*37.

Maple

N:= 10000: # to get all terms <= N
P:= select(isprime, [$1..floor(sqrt(N))]):
Res:= NULL:
for i from 1 to nops(P) do
  for j from 1 to i-1 do
    r:= P[i]^2 + P[j]^2;
    if r > N then break fi;
    if numtheory:-bigomega(r) = 2 then Res:= Res, r fi;
od od:
sort(convert({Res}, list)); # Robert Israel, Nov 03 2017

Mathematica

fQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2; Select[ Sort[ Flatten[ Table[ Prime[p]^2 + Prime[q]^2, {p, 16}, {q, p - 1}]]], fQ[ # ] &] (* Robert G. Wilson v, Mar 23 2005 *)

Prog

(PARI) {m=53; v=[]; forprime(p=2, m, forprime(q=nextprime(p+1), m, if(bigomega(k=p^2+q^2)==2, v=concat(v, k)))); v=vecsort(v); stop=nextprime(m+1)^2; for(j=1, length(v), if(v[j]<stop, print1(v[j], ", ")))} \\ Klaus Brockhaus

Crossrefs

Cf. A001358, A006881, A103739.

Sequence in context: A294173 A176687 A224896 * A103686 A211715 A108610

Adjacent sequences: A103555 A103556 A103557 * A103559 A103560 A103561

Keyword

easy,nonn

Author

Giovanni Teofilatto, Mar 23 2005

Extensions

More terms from Klaus Brockhaus and Robert G. Wilson v, Mar 23 2005

Status

approved