

A220063


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


8



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
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OFFSET

1,1


COMMENTS

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.


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000


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
a(n) = A277459(n) + 2 = A277460(n) + 1.  Bobby Jacobs, Oct 27 2016


EXAMPLE

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.


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 *)


CROSSREFS

Cf. A001358, A219996, A277459, A277460.
Sequence in context: A046298 A258556 A185763 * A135441 A188150 A234227
Adjacent sequences: A220060 A220061 A220062 * A220064 A220065 A220066


KEYWORD

nonn,base


AUTHOR

Jonathan Vos Post, Dec 10 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).
Example corrected by Bobby Jacobs, Sep 28 2016


STATUS

approved



