A220063 Decades whose semiprime pattern is the same as semiprime pattern in the previous decade.
104, 389, 435, 438, 529, 658, 884, 1110, 1183, 1533, 1548, 1557, 1669, 1799, 1824, 1825, 1915, 1993, 2011, 2076, 2085, 2153, 2313, 2355, 2372, 2617, 2628, 2648, 2673, 3204, 3234, 3258, 3280, 3295, 3373, 3415, 3513, 3601, 3636, 3906, 3931, 3936, 4125, 4154
Offset: 1
Examples
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]
Links
- T. D. Noe, Table of n, a(n) for n = 1..1000
Programs
-
Mathematica
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 *) 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 *)
Formula
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
Extensions
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.
Comments