A109406 Numbers n such that (sp(n)+sp(n+1)+sp(n+2))/3 is integer, 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

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A075541.

Sequence in context: A220695 A079258 A134025 * A280632 A178462 A010376

Adjacent sequences: A109403 A109404 A109405 * A109407 A109408 A109409

Keyword

nonn

Author

Zak Seidov, Jun 27 2005

Status

approved