A213025 Balanced semiprimes (of order one): semiprimes which are the average of the previous semiprime and the following semiprime.

34, 86, 94, 122, 142, 185, 194, 202, 214, 218, 262, 289, 302, 314, 321, 358, 371, 394, 407, 413, 415, 422, 446, 471, 489, 493, 497, 517, 535, 562, 581, 586, 626, 634, 669, 687, 698, 734, 785, 791, 815, 838, 842, 922, 982, 989, 1042, 1057, 1079, 1135, 1138

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

194 is in the sequence because 194 = (187 + 194 + 201)/3 = (A001358(61) + A001358(62) + A001358(63))/3.

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

Cf. A086005 (subsequence), A001358, A006562, A065516, A212820.

Sequence in context: A046764 A260276 A278311 * A365200 A086005 A169834

Adjacent sequences: A213022 A213023 A213024 * A213026 A213027 A213028

Keyword

nonn

Author

Gerasimov Sergey, Jun 03 2012

Status

approved