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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. 10

%I

%S 4,415,410111,4101061003,410106100310003,410106100310001100001,

%T 4101061003100011000011000057,410106100310001100001100000110000051,

%U 410106100310001100001100000110000001100000001

%N 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.

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

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

%e a(2) = 415 = 5 * 83 = concatenation of 4 and 15, where 4 is the semiprime 2^2 and 15 is the semiprime 3 * 5.

%e a(3) = 410111 = 13 * 31547 = the concatenation of 4, 10, and 111 where 4 = 2^2, 10 = 2 * 5, and 111 = 3 * 37.

%e a(5) = 410106100310003 = 76871 * 5334991093 = Concatenate(4,10,106,1003,10003).

%Y Cf. A001358, A215641.

%K nonn,base

%O 1,1

%A _Jonathan Vos Post_, Aug 19 2012

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Last modified June 17 12:26 EDT 2021. Contains 345080 sequences. (Running on oeis4.)