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

Author

Jonathan Vos Post, Sep 01 2013

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A000796, A001358, A198019.

Programs

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 *)