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A321219
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Decimal expansion of 2^(-1074).
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2
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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, 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, 5, 5, 0, 7, 2, 7, 0, 2, 0, 8, 7, 5, 1, 8, 6, 5, 2, 9, 9
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OFFSET
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-323,1
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COMMENTS
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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).
The last term is a(427) = 5.
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]
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LINKS
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EXAMPLE
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2^(-1074) = 4.9406564584124654417...*10^(-324).
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MAPLE
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MATHEMATICA
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First[RealDigits[N[2^(-1074), 100], 10]] (* Stefano Spezia, Nov 01 2018 *)
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PROG
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(PARI) a(n) = if(n>=-323&&n<=427, digits(5^1074)[n+324], 0)
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CROSSREFS
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Cf. A307769 (for single-precision floating-point format).
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KEYWORD
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AUTHOR
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STATUS
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approved
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