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A116946 Closest semiprime to n-th semiprime S that is different from S (break ties by taking the smaller semiprime).

%I A116946 #17 Jun 04 2021 09:47:28
%S A116946 6,4,10,9,15,14,22,21,26,25,34,33,34,39,38,49,51,49,57,58,57,65,62,65,
%T A116946 77,74,85,86,85,86,93,94,93,94,111,115,118,119,118,122,121,122,133,
%U A116946 134,133,142,141,142,146,145,158,159,158,159,169,166,178,177,185
%N A116946 Closest semiprime to n-th semiprime S that is different from S (break ties by taking the smaller semiprime).
%H A116946 Michael S. Branicky, <a href="/A116946/b116946.txt">Table of n, a(n) for n = 1..10000</a>
%e A116946 Closest semiprimes to 4, 6, 9, 10, 14, 15, 21 are 6, 4, 10, 9, 15, 14, 22.
%t A116946 csp[{a_,b_,c_}]:=If[c-b<b-a,c,a]; Join[{6},csp/@Partition[Select[Range[ 300], PrimeOmega[#]==2&],3,1]] (* _Harvey P. Dale_, May 06 2014 *)
%o A116946 (Python)
%o A116946 from sympy import factorint
%o A116946 def semiprime(n): return sum(e for e in factorint(n).values()) == 2
%o A116946 def nextsemiprime(n):
%o A116946   nxt = n + 1
%o A116946   while not semiprime(nxt): nxt += 1
%o A116946   return nxt
%o A116946 def aupton(terms):
%o A116946   prv, cur, nxt, alst = 0, 4, 6, []
%o A116946   while len(alst) < terms:
%o A116946     alst.append(prv if 2*cur - prv <= nxt else nxt)
%o A116946     prv, cur, nxt = cur, nxt, nextsemiprime(nxt)
%o A116946   return alst
%o A116946 print(aupton(59)) # _Michael S. Branicky_, Jun 04 2021
%Y A116946 Cf. A001358 (semiprimes), A051701 (analog for primes).
%K A116946 easy,nonn
%O A116946 1,1
%A A116946 _Jonathan Vos Post_, Mar 25 2006
%E A116946 Corrected by _Harvey P. Dale_, May 06 2014