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Numbers k such that k-th prime + k-th semiprime is semiprime.
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%I #13 Nov 16 2023 15:56:50

%S 1,2,3,5,7,10,15,19,22,24,26,27,31,36,41,44,57,60,67,78,84,87,91,93,

%T 101,102,103,104,105,107,115,116,120,121,124,126,128,129,131,135,136,

%U 137,138,140,151,161,168,183,186,189,190,191,195,208,215,225,227,228,231

%N Numbers k such that k-th prime + k-th semiprime is semiprime.

%H Robert Israel, <a href="/A092021/b092021.txt">Table of n, a(n) for n = 1..10000</a>

%e 3 is a member because third prime is 5, third semiprime is 9 and 5+9=14 is semiprime.

%p P:= select(isprime, [2,seq(i,i=3..10000,2)]):

%p S:= select(t -> numtheory:-bigomega(t)=2, [$4..10000]):

%p select(t -> numtheory:-bigomega(P[t]+S[t]) = 2, [$1 .. min(nops(P), nops(S))]); # _Robert Israel_, Nov 15 2023

%Y Cf. A092108.

%K easy,nonn

%O 1,2

%A _Ray Chandler_, Feb 24 2004