A215647 Smallest semiprime whose decimal expansion consists of the concatenation of a 1-digit semiprime, a 2-digit semiprime, a 3-digit semiprime, ..., and an n-digit semiprime.

4, 415, 410111, 4101061003, 410106100310003, 410106100310001100001, 4101061003100011000011000057, 410106100310001100001100000110000051, 410106100310001100001100000110000001100000001

Offset: 1

Author

Jonathan Vos Post, Aug 19 2012

Keywords

• nonn
• base

Comments

This is to A215641 as semiprimes A001358 are to primes A000040. It is a plausible conjecture that a(n) always exists.

If a(n) exists it has A000217(n) = n(n+1)/2 digits.

Examples

			a(2) = 415 = 5 * 83 = concatenation of 4 and 15, where 4 is the semiprime 2^2 and 15 is the semiprime 3 * 5.
a(3) = 410111 = 13 * 31547 = the concatenation of 4, 10, and 111 where 4 = 2^2, 10 = 2 * 5, and 111 = 3 * 37.
a(5) = 410106100310003 = 76871 * 5334991093 = Concatenate(4,10,106,1003,10003).
		

Crossrefs

Cf. A001358, A215641.