NEW SEQUENCE: Semiprime gaps without primes

[Peter Pein]

Dear Zak and seqfans

propably I have got difficulties in understanding the definition.

I get 33 as a(2) because 33=3*11 and 33+2=7*5 and 34 is not prime.

Have a nice Christmas,
Peter

P.S.: a short Mathematica-hack:
In[1]:=
Reap[Block[{n = 1},
 Do[
  If[Plus @@ FactorInteger[i][[All,2]] == 2 &&
     Plus @@ FactorInteger[n + i][[All,2]] == 2,
   If[Select[Range[i, i + n], PrimeQ] == {},
    Sow[i]; n++]],
  {i, 5*10^6}]
]][[2,1]]

Out[1]=
{9,33,55,91,118,203,214,295,469,527,1138,1261,1333,1337,1339,1639,2182,2183,
2479,2481,2974,3139,4299,4835,5353,8391,8894,14109,16145,16147,18807,19337,
19622,20813,22574,25477,31417,31421,31427,31909,34066,34073,35683,43339,44294,
44301,59282,79703,82078,85937,107383,107386,110361,134515,149631,155927,
155941,162145,173363,186487,265641,281433,281434,281443,360662,360667,360674,
370283,370297,370299,535403,537419,841465,843917,843919,860155,982985,1053865,
1098862,1098869,1100978,1138279,1313474,1313479,1444318,1444321,1468286,
1468293,1561946,1561947,1671783,1671803,1671809,1761189,1889843,1889857,
2010742,2010761,2637806,2637807,2898242,3064757,3453838,3826023,3826033,
3826047,3933614,4652359}


zak seidov schrieb:
> Neil, Jack, seqfans,
> any comments?
> thanks, zak
> 
> %I A000001
> %S A000001
> 9,49,62,403,341,843,6722,3473,2869,14059,18467,26603,166126,41779,74491,192061,463161,226489,344119,517421,943606,2171131,4577519,584213,2560177,4356633,8367139,11174753,13191293,7319797,27841051,10644122,13683034,29492893,47735342,26837363
> %N A000001 a(n)=smallest semiprime s1 such that
> between s1 and s2=nextsemiprime(s1)=s1+n there is no
> prime.
> %e A000001 a(1)=9 because between 9 and 10 there is no
> prime,
> a(2)=49 because between 49 and 51 there is no prime, 
> a(3)=62 because between 62 and 65 there is no prime. 
> %O A000001 1
> %K A000001 ,nonn,
> %A A000001 Jack Brennen (jb at brennen.net) and Zak
> Seidov (zakseidov at yahoo.com), Dec 23 2007
> 
> 
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