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%I #10 Dec 29 2021 05:55:58
%S 12,29,33,41,47,64,70,73,96,124,137,194,211,254,277,308,333,372,395,
%T 416,471,507,529,544,560,573,602,624,637,657,672,687,696,716,752,764,
%U 767,869,949,1003,1025,1069,1079,1090,1176,1212,1242,1261,1343,1523,1553
%N Numbers k such that semiprime(k)+/-1 are both semiprime.
%H Michael S. Branicky, <a href="/A174649/b174649.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 12 because 12th semiprime = 2*17, 2*17-1 = 3*11 and 2*17+1 = 5*7;
%e a(2) = 29 because 29th semiprime = 2*43, 2*43-1 = 5*17 and 2*43+1 = 3*29.
%t Flatten[Position[Select[Range[7000],PrimeOmega[#]==2&],_?(PrimeOmega[#-1] == PrimeOmega[#+1]==2&)]] (* _Harvey P. Dale_, Dec 18 2012 *)
%o (Python)
%o from sympy import factorint
%o from itertools import count, islice
%o def semiprimes():
%o for i in count(1):
%o if sum(factorint(i).values()) == 2:
%o yield i
%o def agen():
%o g = semiprimes()
%o prevsp, sp, nextsp = next(g), next(g), next(g)
%o for k in count(2):
%o if nextsp - prevsp == 2:
%o yield k
%o prevsp, sp, nextsp = sp, nextsp, next(g)
%o print(list(islice(agen(), 51))) # _Michael S. Branicky_, Dec 29 2021
%Y Cf. A001358.
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Mar 25 2010
%E Corrected by _Ray Chandler_, Apr 06 2010
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