login
A307533
Primes p such that p+2 has exactly two distinct prime factors.
1
13, 19, 31, 37, 43, 53, 61, 67, 73, 83, 89, 97, 109, 113, 127, 131, 139, 151, 157, 173, 181, 199, 211, 223, 233, 251, 257, 263, 277, 293, 307, 317, 331, 337, 349, 353, 367, 373, 379, 389, 401, 409, 421, 439, 443, 449, 457, 467, 479, 487, 491, 499, 503, 509, 541
OFFSET
1,1
COMMENTS
(13,31), (37,73), (157,751), (199,991) are pairs of emirps belonging to this sequence such that the lesser term of the pair is the reverse of the greater. Are there infinitely many such pairs?
Are there infinitely many triples in the sequence like (61,67,73) and (251,257,263), that is, infinitely many a(n) such that a(n+1)=a(n)+6 and a(n+2)=a(n)+12?
The triples found so far are (61,67,73), (251,257,263) and (367,373,379). The first terms of the triples found are 61, 251 and 367, which belong to the sequence A038107.
LINKS
EXAMPLE
61 is in the sequence because 61 + 2 = 63 has exactly two distinct prime factors (3 and 7).
MAPLE
filter:= proc(n) isprime(n) and nops(numtheory:-factorset(n+2))=2 end proc:
select(filter, [seq(i, i=3..1000, 2)]); # Robert Israel, Jul 28 2019
MATHEMATICA
Select[Range[500], PrimeQ[#] && PrimeNu[# + 2] == 2 &] (* Amiram Eldar, Apr 14 2019 *)
PROG
(PARI) isok(p) = isprime(p) && (omega(p+2) == 2); \\ Michel Marcus, May 02 2019
CROSSREFS
Sequence in context: A108097 A102764 A164318 * A092738 A272382 A376830
KEYWORD
nonn,less
AUTHOR
Paolo Galliani, Apr 13 2019
STATUS
approved