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%I #36 Sep 19 2019 21:47:21
%S 4,9,4,0,6,5,6,4,5,8,4,1,2,4,6,5,4,4,1,7,6,5,6,8,7,9,2,8,6,8,2,2,1,3,
%T 7,2,3,6,5,0,5,9,8,0,2,6,1,4,3,2,4,7,6,4,4,2,5,5,8,5,6,8,2,5,0,0,6,7,
%U 5,5,0,7,2,7,0,2,0,8,7,5,1,8,6,5,2,9,9
%N Decimal expansion of 2^(-1074).
%C Smallest positive representable value in IEEE-754 double-precision floating-point format when subnormal numbers (or denormalized numbers) are supported. See the Wikipedia link below for the double-precision representation of this number (sixty-three 0's and one 1).
%C The last term is a(427) = 5.
%C Some other facts about double-precision numbers: (i) there are 2^64 - 2^53 - 1 = 18437736874454810623 representable numbers, because all 1's in the 11-bit exponent results in positive or negative infinity (depending on the sign bit), and 0 has two representations (all 0's or one 1 followed by sixty-three 0's); (ii) the largest representable number is 2^1024 - 2^971 = 1.7976931348623157...*10^308 (sign bit = 0, exponent = 11111111110, fraction = fifty-two 1's); (iii) the smallest non-representable positive integer is 2^53 + 1 = 9007199254740993. [Extended by _Jianing Song_, Apr 27 2019]
%H Jianing Song, <a href="/A321219/b321219.txt">Table of n, a(n) for n = -323..427</a> (full sequence)
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Double-precision_floating-point_format#Double-precision_examples">Double-precision floating-point format</a>
%e 2^(-1074) = 4.9406564584124654417...*10^(-324).
%p evalf[120](2^(-1074)); # _Muniru A Asiru_, Nov 24 2018
%t First[RealDigits[N[2^(-1074), 100], 10]] (* _Stefano Spezia_, Nov 01 2018 *)
%o (PARI) a(n) = if(n>=-323&&n<=427, digits(5^1074)[n+324], 0)
%Y Cf. A307769 (for single-precision floating-point format).
%K nonn,cons,fini,full
%O -323,1
%A _Jianing Song_, Oct 31 2018
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