A346659 Primes that are not of the form p*q +- 2 where p and q are primes (not necessarily distinct).

3, 5, 29, 43, 61, 73, 101, 103, 107, 137, 149, 151, 173, 191, 193, 197, 227, 229, 241, 271, 277, 281, 283, 313, 347, 349, 421, 431, 433, 457, 461, 463, 523, 569, 601, 607, 617, 619, 641, 643, 659, 661, 727, 821, 823, 827, 857, 859, 883, 929, 1019, 1021, 1031

Offset

1,1

Comments

Conjecture: this sequence is infinite.

Links

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

Example

2 is not a term because 2 = 2*2 - 2.
3 is a term because neither 1 (3-2) nor 5 (3+2) is a product of two primes.

Maple

q:= n-> andmap(x-> numtheory[bigomega](x)<>2, [n-2, n+2]):
select(q, [ithprime(i)$i=1..200])[];  # Alois P. Heinz, Jul 30 2021

Mathematica

Select[Range[3, 1000], PrimeQ[#] && PrimeOmega[# - 2] != 2 && PrimeOmega[# + 2] != 2 &] (* Amiram Eldar, Jul 29 2021 *)

Prog

(Python)
from sympy import factorint, primerange
def semiprime(n): return sum(e for e in factorint(n).values()) == 2
def ok(p): return not semiprime(p-2) and not semiprime(p+2)
def aupto(limit): return list(filter(ok, primerange(1, limit+1)))
print(aupto(1031)) # Michael S. Branicky, Jul 29 2021

Crossrefs

Cf. A207526 (complementary sequence).

Sequence in context: A272345 A356147 A364762 * A067200 A106089 A303971

Adjacent sequences: A346656 A346657 A346658 * A346660 A346661 A346662

Keyword

nonn

Author

Marcin Barylski, Jul 27 2021

Extensions

More terms from Michael S. Branicky, Jul 29 2021

Status

approved