OFFSET
-44,2
COMMENTS
Smallest positive representable value in IEEE-754 single-precision floating-point format when subnormal numbers (or denormalized numbers) are supported. See the Wikipedia link below for the single-precision representation of this number (thirty-one 0's and one 1).
This is the full sequence.
Some other facts about single-precision numbers: (i) there are 2^32 - 2^24 - 1 = 4278190079 representable numbers, because all 1's in the 8-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 thirty-one 0's); (ii) the largest representable number is 2^128 - 2^104 = 340282346638528859811704183484516925440 (sign bit = 0, exponent = 11111110, fraction = twenty-three 1's); (iii) the smallest non-representable positive integer is 2^24 + 1 = 16777217.
LINKS
EXAMPLE
2^(-149) = 1.40129846432481...*10^(-45).
PROG
(PARI) a(n) = if(n>=-44&&n<=60, digits(5^149)[n+45], 0)
CROSSREFS
KEYWORD
AUTHOR
Jianing Song, Apr 27 2019
STATUS
approved