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%I #8 Mar 30 2012 18:40:57
%S 10,121,123,1234,123451,1234561,1234567,123456782,12345678911,
%T 123456789101,123456789101117,12345678910111229,123456789101112133,
%U 123456789101112131414,1234567891011121314159
%N Smallest semiprime containing leading sequence of n ascending numbers.
%C This is to semiprimes A001358 as A053546 is to primes A000040.
%e a(1) = 10 because 10 = 2 * 5 is the smallest semiprime (or biprime, products of two primes) whose leftmost (base 10) digit is 1.
%e a(2) = 121 because 121 = 11^2 semiprime whose leftmost digits are 12.
%e a(3) = 123 since it is a semiprime already.
%e a(4) = 1234 = 2 * 617.
%e a(5) = 123451 = 41 * 3011.
%e a(6) = 1234561 = 211 * 5851.
%t semiPrimeQ[n_] := Plus @@ Last /@ FactorInteger@ n == 2; f[n_] := Block[{k = 0, m = FromDigits@ Flatten@ IntegerDigits@ Range@ n}, If[ semiPrimeQ@ m, , While[a = 10^(1 + Max[0, Floor@ Log10@ k]) m + k; ! semiPrimeQ@ a, k++]; m = a]; m]; Array[f, 15]
%Y Cf. A001358, A053546, A100959.
%K nonn,easy
%O 1,1
%A _Jonathan Vos Post_, Dec 30 2010