A307769 Decimal expansion of 2^(-149).

1, 4, 0, 1, 2, 9, 8, 4, 6, 4, 3, 2, 4, 8, 1, 7, 0, 7, 0, 9, 2, 3, 7, 2, 9, 5, 8, 3, 2, 8, 9, 9, 1, 6, 1, 3, 1, 2, 8, 0, 2, 6, 1, 9, 4, 1, 8, 7, 6, 5, 1, 5, 7, 7, 1, 7, 5, 7, 0, 6, 8, 2, 8, 3, 8, 8, 9, 7, 9, 1, 0, 8, 2, 6, 8, 5, 8, 6, 0, 6, 0, 1, 4, 8, 6, 6, 3, 8, 1, 8, 8, 3, 6, 2, 1, 2, 1, 5, 8, 2, 0, 3, 1, 2, 5

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

Table of n, a(n) for n=-44..60.

Wikipedia, Single-precision floating-point format

Example

2^(-149) = 1.40129846432481...*10^(-45).

Prog

(PARI) a(n) = if(n>=-44&&n<=60, digits(5^149)[n+45], 0)

Crossrefs

Cf. A321219 (for double-precision floating-point format).

Sequence in context: A196817 A229987 A343953 * A096793 A155998 A298063

Adjacent sequences: A307766 A307767 A307768 * A307770 A307771 A307772

Keyword

nonn,cons,fini,full

Author

Jianing Song, Apr 27 2019

Status

approved