A106557 Largest number that can be obtained by concatenating the two factors of the n-th semiprime.

22, 32, 33, 52, 72, 53, 73, 211, 55, 213, 311, 217, 75, 219, 313, 232, 77, 317, 511, 319, 292, 312, 513, 323, 372, 711, 412, 517, 432, 329, 713, 331, 472, 519, 532, 373, 523, 592, 717, 1111, 612, 413, 433, 719, 672, 473, 712, 1311, 529, 732, 531, 792, 533

Offset: 1

Author

Eric Angelini, May 09 2005

Keywords

• base
• easy
• nonn

Examples

			First semiprime is 4; 4 is 2*2 -> 22.
Second semiprime is 6; 6 is 3*2 -> 32 (and not 23).
...
Eighth semiprime is 22; 22 is 2*11 -> 211 (and not 112).
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001358, A084797, A106556.

Programs

PARI

\\ here cd(x,y) returns base 10 concatenation.
cd(v1, v2)={10^(logint(v2,10) + 1)*v1 + v2}
seq(n)={my(v=vector(n), k=0); for(i=1, #v, k++; while(2<>bigomega(k), k++); my(f=factor(k)[,1]); v[i] = if(#f==1, cd(f[1], f[1]), max(cd(f[1], f[2]), cd(f[2], f[1])))); v} \\ Andrew Howroyd, Jan 08 2020

Formula

a(n) = A084797(A001358(n)). - Andrew Howroyd, Jan 08 2020

Extensions

Edited by N. J. A. Sloane, Apr 14 2008

Terms a(22) and beyond from Andrew Howroyd, Jan 08 2020