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

1,1

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: A299218 A300032 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