OFFSET
1,1
COMMENTS
Semiprimes that are the average of three successive semiprimes.
First term not also in A086005 is 185. - Alonso del Arte, Jun 04 2012
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Semiprime
FORMULA
2*sp_(n) = sp_(n - 1) + sp_(n + 1).
a(n) = 1/3 * (sp(i) + sp(i + 1) + sp(i + 2), for some i(n).
EXAMPLE
MAPLE
with(numtheory):
prevsp:= proc(n) local k; for k from n-1 by -1
while isprime(k) or bigomega(k)<>2 do od; k end:
nextsp:= proc(n) local k; for k from n+1
while isprime(k) or bigomega(k)<>2 do od; k end:
a:= proc(n) option remember; local s;
s:= `if`(n=1, 4, a(n-1));
do s:= nextsp(s);
if s=(prevsp(s)+nextsp(s))/2 then break fi
od; s
end:
seq (a(n), n=1..100); # Alois P. Heinz, Jun 03 2012
MATHEMATICA
bspQ[{a_, b_, c_}]:=b==(a+c)/2; With[{sp=Select[Range[1200], PrimeOmega[#] == 2&]}, Transpose[Select[Partition[sp, 3, 1], bspQ]][[2]]] (* Harvey P. Dale, Nov 18 2012 *)
PROG
(Haskell)
a213025 n = a213025_list !! (n-1)
a213025_list = f a001358_list where
f (x:sps'@(y:z:sps)) | 2 * y == (x + z) = y : f sps'
| otherwise = f sps'
-- Reinhard Zumkeller, Jun 10 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Gerasimov Sergey, Jun 03 2012
STATUS
approved