A336781 -id:A336781 - cp's OEIS frontend

A336776 a(n) is the least number of repetitions such that the result of the repeated execution of the multiplication f <- f*n started at f=1 produces an overflow, when the multiplication is performed using 32-bit single precision floats according to the IEEE 754 standard.

128, 81, 64, 56, 50, 46, 43, 41, 39, 38, 36, 35, 34, 33, 32, 32, 31, 31, 30, 30, 29, 29, 28, 28, 28, 27, 27, 27, 27, 26, 26, 26, 26, 25, 25, 25, 25, 25, 25, 24, 24, 24, 24, 24, 24, 24, 23, 23, 23, 23, 23, 23, 23, 23, 23, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 21

Offset: 2

Hugo Pfoertner, Aug 07 2020

See A336774 for more information and links.

The overflow usually raises the corresponding exception, with +infinity returned as result.

Hugo Pfoertner, Comparison with 128-bit results, range n=2..128, computed on x86-64 architecture.

Cf. A336774, A336775, A336777, A336778, A336779, A336780, A336781.

A336780 a(n) is the least number of repetitions such that the result of the repeated execution of the multiplication f <- f*n started at f=1 produces an overflow, when the multiplication is performed using 64-bit double precision floats according to the IEEE 754 standard.

Original entry on oeis.org

1024, 647, 512, 442, 397, 365, 342, 324, 309, 297, 286, 277, 269, 263, 256, 251, 246, 242, 237, 234, 230, 227, 224, 221, 218, 216, 214, 211, 209, 207, 205, 203, 202, 200, 199, 197, 196, 194, 193, 192, 190, 189, 188, 187, 186, 185, 184, 183, 182, 181, 180, 179, 178

Offset: 2

Hugo Pfoertner, Aug 07 2020

See A336774 for more information and links.

The overflow usually raises the corresponding exception, with +infinity returned as result.

Hugo Pfoertner, Comparison with 128-bit results, range n=2..128, computed on x86-64 architecture.

Cf. A336774, A336775, A336776, A336777, A336778, A336779, A336781.

A336777 a(n) is the least number of repetitions such that the result of the repeated execution of the division f <- f/n started at f=1 produces 0, when the division is performed using 32-bit single precision floats according to the IEEE 754 standard.

Original entry on oeis.org

151, 96, 76, 66, 59, 55, 51, 49, 47, 45, 43, 42, 41, 40, 39, 38, 37, 37, 36, 36, 35, 35, 34, 34, 33, 33, 33, 32, 32, 32, 31, 31, 31, 31, 31, 30, 30, 30, 30, 29, 29, 29, 29, 29, 29, 29, 28, 28, 28, 28, 28, 28, 28, 27, 27, 27, 27, 27, 27, 27, 27, 27, 26, 26, 26, 26

Offset: 2

Hugo Pfoertner, Aug 07 2020

See A336774 for more information and links.

In contrast to multiplication (A336776), a larger range of values can be used in division by using leading zeros in the significands. The underflow gap is filled by using denormal numbers, also called subnormal numbers.

Hugo Pfoertner, Comparison with 128-bit results, range n=2..128, computed on x86-64 architecture.
Wikipedia, Denormal number.

Cf. A336774, A336775, A336776, A336778, A337779, A336780, A336781.

A337068 a(n) is the least number of repetitions such that the result of the repeated execution of the division f <- f/n started at f=1 produces 0, when the division is performed using Commodore BASIC.

Original entry on oeis.org

129, 81, 65, 56, 50, 46, 43, 41, 39, 38, 36, 35, 34, 33, 33, 32, 31, 31, 30, 30, 29, 29, 28, 28, 28, 27, 27, 27, 27, 26, 26, 26, 26, 25, 25, 25, 25, 25, 25, 24, 24, 24, 24, 24, 24, 24, 23, 23, 23, 23, 23, 23, 23, 23, 23, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22

Offset: 2

Markus Sigg, Aug 13 2020

A floating point number in Commodore BASIC has five bytes: one bit for the sign, 31 bits for the mantissa, eight bits for the exponent.

C64 Wiki, Floating point arithmetic
Markus Sigg, Initial terms, displayed on original Commodore 2001 hardware.
Markus Sigg, Screenshot of the program running on a PET 2001 emulated with MAME.
Wikipedia, Commodore BASIC

Cf. A336777, A336781.

10 FOR N=2 TO 66
20 A=1
30 I=1
40 A=A/N
50 IF A>0 THEN I=I+1:GOTO 40
60 PRINT I;
70 NEXT

cp's OEIS Frontend

A336776 a(n) is the least number of repetitions such that the result of the repeated execution of the multiplication f <- f*n started at f=1 produces an overflow, when the multiplication is performed using 32-bit single precision floats according to the IEEE 754 standard.

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A336780 a(n) is the least number of repetitions such that the result of the repeated execution of the multiplication f <- f*n started at f=1 produces an overflow, when the multiplication is performed using 64-bit double precision floats according to the IEEE 754 standard.

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A336777 a(n) is the least number of repetitions such that the result of the repeated execution of the division f <- f/n started at f=1 produces 0, when the division is performed using 32-bit single precision floats according to the IEEE 754 standard.

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A337068 a(n) is the least number of repetitions such that the result of the repeated execution of the division f <- f/n started at f=1 produces 0, when the division is performed using Commodore BASIC.

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BASIC