A109406 Numbers m such that (sp(m)+sp(m+1)+sp(m+2))/3 is an integer, where sp(n) = n-th semiprime.
3, 4, 9, 10, 11, 14, 20, 28, 29, 32, 34, 40, 43, 44, 45, 46, 50, 53, 58, 59, 61, 62, 63, 68, 69, 72, 74, 80, 83, 86, 89, 95, 99, 100, 101, 105, 107, 109, 111, 112, 115, 116, 118, 119, 121, 123, 127, 129, 130, 131, 132, 136, 137, 140, 144, 145, 150, 151, 152, 153, 155
Offset: 1
Keywords
Examples
3 is OK because (sp(3)+sp(4)+sp(5))/3=(9+10+14)/3 = 11; sp(n) = n-th semiprime.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Crossrefs
Cf. A075541.
Programs
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Mathematica
Flatten[Position[Partition[Select[Range[600],PrimeOmega[#]==2&],3,1], ?( IntegerQ[ Total[#]/3]&),{1},Heads->False]] (* _Harvey P. Dale, Jan 23 2016 *)
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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