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A346659 Primes that are not of the form p*q +- 2 where p and q are primes (not necessarily distinct). 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: this sequence is infinite.

LINKS

Table of n, a(n) for n=1..53.

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: A141578 A327748 A272345 * A067200 A106089 A303971

Adjacent sequences:  A346656 A346657 A346658 * A346660 A346661 A346663

KEYWORD

nonn

AUTHOR

Marcin Barylski, Jul 27 2021

EXTENSIONS

More terms from Michael S. Branicky, Jul 29 2021

STATUS

approved

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Last modified November 27 20:49 EST 2021. Contains 349395 sequences. (Running on oeis4.)