A226943 Semiprimes in the order in which they appear in the decimal expansion of Pi.

4, 14, 314, 141, 15, 415, 1415, 9, 159, 6, 26, 926, 5926, 15926, 65, 265, 2653, 92653, 592653, 35, 535, 6535, 5926535, 58, 358, 265358, 314159265358, 589, 3589, 53589, 2653589, 92653589, 1592653589, 1415926535897, 979, 5358979, 59265358979, 159265358979

Offset

1,1

Comments

This is to semiprimes A001358 as A198019 is to primes A000040. Considering the first 1, 2, 3, 4, ... digits of the decimal expansion 3.14159... of Pi, record the semiprimes that have not occurred earlier, the smaller first if two or more appear by the n-th digit that have not been seen in the first n-1 digits.

Links

Giovanni Resta, Table of n, a(n) for n = 1..300

Example

There are no semiprimes in the first 1 or 2 digits (3, 31). Then after 3 digits we have three: 4, 14, and 314 appearing for the first time. So a(1) = 4, a(2) = 14 and a(3) = 314.

Mathematica

semiQ[n_] := Total[Last /@ FactorInteger@n ] == 2; sp = Select[Range@ 999, semiQ]; spQ[n_] := If[n < 10^6, semiQ@n, ! Or @@ IntegerQ /@ (n/sp) && semiQ@ n]; seq = {}; Do[seq = Join[seq, Select[Union@ Complement[ Mod[FromDigits@ RealDigits[Pi, 10, n][[1]], 10^Range[n, 1, -1]], seq], spQ]], {n, 30}]; seq (* Giovanni Resta, Oct 01 2013 *)

Crossrefs

Cf. A000796, A001358, A198019.

Sequence in context: A129226 A003010 A118770 * A292708 A367534 A112514

Adjacent sequences: A226940 A226941 A226942 * A226944 A226945 A226946

Keyword

nonn,base

Author

Jonathan Vos Post, Sep 01 2013

Status

approved