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A220063 Decades whose semiprime pattern is the same as semiprime pattern in the previous decade.

%I A220063 #60 Nov 01 2024 05:06:06
%S A220063 104,389,435,438,529,658,884,1110,1183,1533,1548,1557,1669,1799,1824,
%T A220063 1825,1915,1993,2011,2076,2085,2153,2313,2355,2372,2617,2628,2648,
%U A220063 2673,3204,3234,3258,3280,3295,3373,3415,3513,3601,3636,3906,3931,3936,4125,4154
%N A220063 Decades whose semiprime pattern is the same as semiprime pattern in the previous decade.
%C A220063 This is to 10 and semiprimes A001358 as A219996 is to 100 and primes A000040. The first decade (1,2,3,4,5,6,7,8,9,10) has a unique pattern, as no decade ending with a multiple k*10 for k>1 ends with a semiprime; so it does not matter whether 10 is at the beginning or the end of a decade.
%H A220063 T. D. Noe, <a href="/A220063/b220063.txt">Table of n, a(n) for n = 1..1000</a>
%F A220063 a(n) ~ n. In particular there are x - 200x log log x/log x + O(x/log x) members of this sequence below x. - _Charles R Greathouse IV_, Dec 11 2012
%F A220063 a(n) = A277459(n) + 2 = A277460(n) + 1. - _Bobby Jacobs_, Oct 27 2016
%e A220063 a(1) = 104 because the decade (1030..1039) has the same semiprime pattern as the previous decade: (1020..1029), namely that each has only a single semiprime, respectively 1027 = 13 * 79 and 1037 = 17 * 61. [corrected by _Bobby Jacobs_, Sep 28 2016]
%t A220063 SemiPrimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; nn = 50000; s = Table[SemiPrimeQ[n], {n, nn}]; t = Partition[s, 10]; t2 = {}; Do[If[t[[i]] == t[[i - 1]], AppendTo[t2, i]], {i, 2, Length[t]}]; t2 (* _T. D. Noe_, Dec 11 2012 *)
%t A220063 semiPrimeQ[n_] := PrimeOmega@ n == 2; f[n_] := semiPrimeQ@# & /@ (10 n + Range@9); a = f[0]; k = 1; lst = {}; While[k < 10001, b = f[k]; If[a == b, AppendTo[lst, k]]; a = b; k++]; lst (* _Robert G. Wilson v_, Dec 11 2012 *)
%Y A220063 Cf. A001358, A219996, A277459, A277460.
%K A220063 nonn,base
%O A220063 1,1
%A A220063 _Jonathan Vos Post_, Dec 10 2012
%E A220063 All terms from _T. D. Noe_, Dec 11 2012, and (with 1 already added to each) all terms after the first from _Robert G. Wilson v_, by email to _Jonathan Vos Post_.