A321788 Product of semiprime factors using lunar arithmetic.

2, 2, 3, 2, 2, 3, 3, 11, 5, 12, 11, 12, 5, 12, 13, 22, 7, 13, 11, 13, 22, 21, 13, 23, 22, 11, 21, 15, 22, 23, 13, 31, 22, 15, 22, 33, 23, 22, 17, 111, 21, 31, 33, 17, 22, 33, 21, 111, 25, 22, 31, 22, 33, 23, 22, 113, 33, 22, 31, 35, 111, 22, 33, 101, 27, 41, 102, 111, 31, 102, 43, 31, 102, 33, 113, 112, 45

Offset: 1

Author

G. L. Honaker, Jr., Nov 18 2018

Keywords

• nonn
• base

Examples

			a(16)=22 because the 16th semiprime is 46 = 2*23. In lunar arithmetic the product becomes 22.
		

Links

• Metin Sariyar, Table of n, a(n) for n = 1..10000
• D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic, Journal of Integer Sequences, Vol. 14 (2011), Article 11.9.8. [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
• Caldwell and Honaker, Prime Curio for 58.

Crossrefs

Cf. A001358, A087062, A084126, A084127.

Programs

Mathematica

ladd[x_, y_] := FromDigits[MapThread[Max, IntegerDigits[#, 10, Max@ IntegerLength [{x, y}]] & /@ {x, y}]]; lmult[x_, y_] := Fold[ladd, 0, Table[10^i, {i, IntegerLength[y] - 1, 0, -1}]*FromDigits /@ Transpose@Partition[Min[##] & @@@ Tuples[IntegerDigits[{x, y}]], IntegerLength[y]]]; s={}; Do[If[PrimeOmega[n]==2, f=FactorInteger[n]; x=f[[1,1]]; y=n/x; m=lmult[x,y]; AppendTo[s, m]],{n,1,300}]; s (* Amiram Eldar, Nov 19 2018 after Davin Park at A087062 *)

Formula

a(n) = A087062(A084126(n), A084127(n)). - Michel Marcus, Nov 20 2018