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

Author

Marcin Barylski, Jul 27 2021

Keywords

• nonn

Comments

Conjecture: this sequence is infinite.

Examples

			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.
		

Links

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

Crossrefs

Cf. A207526 (complementary sequence).

Programs

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 *)

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

Extensions

More terms from Michael S. Branicky, Jul 29 2021