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A213025 Balanced semiprimes (of order one): semiprimes which are the average of the previous semiprime and the following semiprime. 4
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 (list; graph; refs; listen; history; text; internal format)
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 * A086005 A169834 A248201

Adjacent sequences:  A213022 A213023 A213024 * A213026 A213027 A213028

KEYWORD

nonn

AUTHOR

Gerasimov Sergey, Jun 03 2012

STATUS

approved

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Last modified July 25 04:48 EDT 2017. Contains 289779 sequences.