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%I #6 Jul 30 2015 23:21:17
%S 0,4,0,2,5,3,6,5,0,5,3,5,6,7,8,1,0,7,7,3,1,0,1,2,5,0,6,7,9,0,2,6,3,2,
%T 7,6,0,2,5,0,7,6,7,5,2,6,7,7,8,0,9,7,7,0,7,0,3,1,2,7,5,4,0,5,6,7,3,7,
%U 5,1,1,8,9,5,1,7,1,9,7,9,1,9,2,9,4,0,2,1,5,0,4,8,8,8,5,8,7,5,6,5,1,5,9,0,4
%N n-th decimal digit of the fractional part of the square root of the n-th semiprime.
%C This is to semiprimes A001358 as A071901 is to prime A000040. Regarded as a decimal fraction, 0.0402536505356781... is likely to be an irrational number.
%e semiprime(1) = 4, sqrt(4) = 2.000, first digit of fractional part is 0, so a(1) = 0.
%e semiprime(2) = 6, sqrt(6) = 2.449, 2nd digit of fractional part is 4, so a(2) = 4.
%e semiprime(3) = 9, sqrt(9) = 3.000, 3rd digit of fractional part is 0, so a(3) = 0.
%e semiprime(4) = 10, sqrt(10) = 3.162277, 4th digit of fractional part is 2, so a(4) = 2.
%e semiprime(5) = 14, sqrt(14) = 3.741657, 5th digit of fractional part is 5, so a(5) = 5.
%e semiprime(6) = 15, sqrt(15) = 3.8729833, 6th digit of fractional part is 3, so a(6) = 3 semiprime(7) = 21, sqrt(21) = 4.58257569, 7th digit of fractional part is 6, so a(6) = 6.
%t SemiPrimePi[n_] := Sum[ PrimePi[n/Prime@i] - i + 1, {i, PrimePi@ Sqrt@n}]; SemiPrime[n_] := Block[{e = Floor[ Log[2, n] + 1], a, b}, a = 2^e; Do[b = 2^p; While[ SemiPrimePi@a < n, a = a + b]; a = a - b/2, {p, e, 0, -1}]; a + b/2]; f[n_] := Mod[ Floor@ N[10^n*Sqrt@ SemiPrime@n, n + 10], 10]; Array[f, 111] (* _Robert G. Wilson v_, Jul 31 2010 *)
%Y Cf. A000040, A001358, A071901.
%K base,easy,nonn
%O 1,2
%A _Jonathan Vos Post_, Jun 22 2010
%E a(16) onwards from _Robert G. Wilson v_, Jul 31 2010
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