login
A355803
Lower twin primes p such that p*(p+2)+p-1, p*(p+2)+p+1 and p*(p+2)+p+3 have at most four distinct prime factors between them.
1
3, 5, 137, 5639, 13397, 33599, 178247, 181607, 255467, 380867, 415379, 439007, 486677, 670037, 931727, 970787, 1163717, 1244987, 1259537, 1343057, 1384067, 1453547, 1540709, 1596347, 1619417, 1793357, 1908659, 2027897, 2097479, 2161637, 2276999, 2840777, 3163967, 3327167, 3536789, 3633347
OFFSET
1,1
COMMENTS
One of the prime factors must be 3.
LINKS
EXAMPLE
a(3) = 137 is a term because 137 and 139 are primes and 137*139+137-1 = 19179 = 3^2 * 2131, 137*139+137+1 = 19181 and 137*139+137+3 = 19183 have the four prime factors 3, 2131, 19181 and 19183.
MAPLE
R:= 3: count:= 1:
for p from 5 by 6 while count < 40 do
if isprime(p) and isprime(p+2) and nops(numtheory:-factorset(p^2+3*p-1) union numtheory:-factorset(p^2+3*p+1)
union numtheory:-factorset(p^2+3*p+3)) <= 4 then
count:= count+1; R:= R, p;
fi;
od:
R;
MATHEMATICA
Select[Prime[Range[250000]], PrimeQ[# + 2] && Length[Union[(Join @@ FactorInteger[#^2 + 3*# + {-1, 1, 3}])[[;; , 1]]]] <= 4 &] (* Amiram Eldar, Jul 20 2022 *)
CROSSREFS
Cf. A001359.
Sequence in context: A088269 A164371 A225672 * A240125 A372746 A108013
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Jul 17 2022
STATUS
approved