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A109805 a(n) = prime(n+2)*prime(n+1) - prime(n)*prime(n+1).

%I A109805 #20 Sep 20 2021 09:04:15
%S A109805 9,20,42,66,78,102,114,230,232,248,370,246,258,470,636,472,488,670,
%T A109805 426,584,790,830,1246,1164,606,618,642,654,2034,2286,1310,1096,1668,
%U A109805 1788,1208,1884,1630,1670,2076,1432,2172,2292,1158,1182,2786,5064,3568,1362
%N A109805 a(n) = prime(n+2)*prime(n+1) - prime(n)*prime(n+1).
%C A109805 9 is the only semiprime of the form prime(n+2)*prime(n+1) - prime(n)*prime(n+1).
%C A109805 First differences of A006094. [_Reinhard Zumkeller_, Mar 13 2011]
%H A109805 Vincenzo Librandi, <a href="/A109805/b109805.txt">Table of n, a(n) for n = 1..1000</a>
%t A109805 Table[Prime[n + 1]*(Prime[n + 2] - Prime[n]), {n, 48}] (* _Ray Chandler_, Aug 17 2005 *)
%t A109805 #[[2]](#[[3]]-#[[1]])&/@Partition[Prime[Range[50]],3,1] (* _Harvey P. Dale_, Apr 01 2018 *)
%o A109805 (Python)
%o A109805 from sympy import prime, primerange
%o A109805 def aupton(nn):
%o A109805     alst, prevp, prev_prod = [], 2, 6
%o A109805     for p in primerange(3, prime(nn+2)+1):
%o A109805         cur_prod = prevp * p
%o A109805         alst.append(cur_prod - prev_prod)
%o A109805         prevp = p
%o A109805         prev_prod = cur_prod
%o A109805     return alst[1:]
%o A109805 print(aupton(48)) # _Michael S. Branicky_, Sep 20 2021
%Y A109805 Cf. A006094.
%Y A109805 The largest prime factor of a(n) gives the sequence A065091.
%K A109805 easy,nonn
%O A109805 1,1
%A A109805 _Giovanni Teofilatto_, Aug 16 2005
%E A109805 Edited and extended by _Ray Chandler_, Aug 17 2005