

A082130


Numbers k such that 2*k1 and 2*k+1 are semiprimes.


4



17, 25, 28, 43, 46, 47, 60, 61, 71, 72, 80, 92, 93, 101, 102, 107, 108, 109, 110, 118, 124, 133, 144, 145, 150, 151, 152, 160, 161, 164, 170, 196, 197, 206, 207, 208, 223, 226, 235, 236, 258, 259, 264, 267, 268, 272, 276, 290, 291, 295, 317, 334, 335, 340, 343, 344
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OFFSET

1,1


COMMENTS

Let p and q be distinct odd primes, and take a and b so that a*p  b*q = 1. Dickson's conjecture implies there are infinitely many k such that 2*a+k*q and 2*b+k*p are prime, in which case n = a*p + (k*q*p1)/2 is in the sequence with 2*n1 = (2*b+k*p)*q and 2*n+1 = (2*a+k*q)*p.  Robert Israel, Aug 13 2018


LINKS



EXAMPLE

17 is a term because 2*17  1 = 33 = 3*11 and 2*17 + 1 = 35 = 5*7 are both semiprimes.


MAPLE

OSP:= select(numtheory:bigomega=2, {seq(i, i=3..1000, 2)}):
R:= map(t > (t+1)/2, OSP intersect map(``, OSP, 2)):


PROG

(PARI) isok(n) = (bigomega(2*n1) == 2) && (bigomega(2*n+1) == 2); \\ Michel Marcus, Jul 16 2017
(Python)
from sympy import factorint
from itertools import count, islice
def agen(): # generator of terms
nxt = 0
for k in count(2, 2):
prv, nxt = nxt, sum(factorint(k+1).values())
if prv == nxt == 2: yield k//2


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



