A290435 Semiprimes of the form pq where p < q and p+q+1 is prime.
21, 35, 39, 55, 57, 65, 77, 85, 111, 115, 129, 155, 161, 185, 187, 201, 203, 205, 209, 221, 235, 237, 265, 291, 299, 305, 309, 319, 323, 327, 335, 341, 365, 371, 377, 381, 391, 413, 415, 437, 451, 485, 489, 493, 497, 505, 515, 517, 535, 579, 611, 623, 649, 655
Offset: 1
Keywords
Examples
655 = 5*131 and 5+131+1 is prime, so 655 is a term.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
With[{nn = 54}, Take[#, nn] &@ Union@ Flatten@ Table[Function[p, Map[Times @@ # &@ # &, #] &@ Select[Map[{p, #} &, Prime@ Range[PrimePi@ p - 1]], PrimeQ[Total@ # + 1] &]]@ Prime@ n, {n, nn + 4}]] (* Michael De Vlieger, Aug 01 2017 *) With[{nn=60},Take[Times@@@Select[Subsets[Prime[Range[nn]],{2}],PrimeQ[ Total[ #]+ 1]&]//Union,nn]] (* Harvey P. Dale, Aug 02 2017 *) -
PARI
isok(n) = (bigomega(n)==2) && (omega(n)==2) && isprime(1+vecsum(factor(n)[,1])); \\ Michel Marcus, Aug 02 2017
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Python
from sympy import factorint, isprime A290435_list = [n for n in range(2,10**5) if sum(factorint(n).values()) == len(factorint(n)) == 2 and isprime(1+sum(factorint(n).keys()))]
Comments