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Numbers n such that (sp(n)+sp(n+1)+sp(n+2))/3 is integer, sp(n) = n-th semiprime.
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%I #7 Jan 23 2016 11:36:05

%S 3,4,9,10,11,14,20,28,29,32,34,40,43,44,45,46,50,53,58,59,61,62,63,68,

%T 69,72,74,80,83,86,89,95,99,100,101,105,107,109,111,112,115,116,118,

%U 119,121,123,127,129,130,131,132,136,137,140,144,145,150,151,152,153,155

%N Numbers n such that (sp(n)+sp(n+1)+sp(n+2))/3 is integer, sp(n) = n-th semiprime.

%H Harvey P. Dale, <a href="/A109406/b109406.txt">Table of n, a(n) for n = 1..1000</a>

%e 3 is OK because (sp(3)+sp(4)+sp(5))/3=(9+10+14)/3 = 11; sp(n) = n-th semiprime.

%t Flatten[Position[Partition[Select[Range[600],PrimeOmega[#]==2&],3,1], _?( IntegerQ[ Total[#]/3]&),{1},Heads->False]] (* _Harvey P. Dale_, Jan 23 2016 *)

%o (PARI) lista(nn) = {vec = vector(nn, i, i); sp = select(i->(bigomega(i)==2), vec); for (i = 1, #sp-2, if (((sp[i]+sp[i+1]+sp[i+2]) % 3) == 0, print1(i, ", ")););} \\ _Michel Marcus_, Oct 06 2013

%Y Cf. A075541.

%K nonn

%O 1,1

%A _Zak Seidov_, Jun 27 2005