A119603 Merging prime factors of n-th composite number.

22, 23, 222, 33, 25, 223, 27, 35, 2222, 233, 225, 37, 211, 2223, 55, 213, 333, 227, 235, 22222, 311, 217, 57, 2233, 219, 313, 2225, 237, 2211, 335, 223, 22223, 77, 255, 317, 2213, 2333, 511, 2227, 319, 229, 2235, 231, 337, 222222, 513, 2311, 2217, 323, 257

Offset: 1

Author

Zak Seidov, Jun 03 2006

Keywords

• nonn
• base

Comments

Rule "replace n-th composite number by concatenation of its prime factors" in A037271; composite numbers A002808.

Examples

			a(6)=223 because 6th composite number is 12: A002808(6)=12, then 12=2*2*3 and merging prime factors we get a(6)=223.
		

Crossrefs

Cf. A002808, A037271, A037276.

Programs

Mathematica

Reap[Do[If[!PrimeQ[n],Sow[FromDigits@Flatten[Table[IntegerDigits[ #[[1]]],{#[[2]]}]&/@FactorInteger@(n)]]],{n,2,115}]][[2,1]]

Formula

a(n) = A037276(A002808(n)). - Jason Yuen, Jun 28 2025