A336779 -id:A336779 - cp's OEIS frontend

A336774 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 differs from the exact value n^a(n), when the multiplication is performed using 32-bit single precision floats according to the IEEE 754 standard.

128, 16, 64, 11, 16, 9, 43, 8, 11, 7, 16, 7, 9, 7, 32, 6, 8, 6, 11, 6, 7, 6, 16, 6, 7, 6, 9, 5, 7, 5, 26, 5, 6, 5, 8, 5, 6, 5, 11, 5, 6, 5, 7, 5, 6, 5, 16, 5, 6, 5, 7, 5, 6, 5, 9, 5, 5, 5, 7, 5, 5, 5, 22, 4, 5, 4, 6, 4, 5, 4, 8, 4, 5, 4, 6, 4, 5, 4, 11, 4, 5, 4

Offset: 2

Hugo Pfoertner, Aug 04 2020

For n a power of two the first deviation is caused by exceeding the maximum representable number of the binary32 single precision floating point format.

Hugo Pfoertner, Table of n, a(n) for n = 2..16384
Hugo Pfoertner, Comparison with exact results, range n=2..128, computed on x86-64 architecture.
Edmund Weitz, IEEE 754 Calculator, uses JavaScript (2016).
Wikipedia, IEEE 754.

Cf. A336775, A336778, A336779.

A336775 a(n) is the largest power of n such that all numbers n^k <= a(n), k=1,..,A336774(n)-1 can be exactly represented as single precision 32-bit floating point numbers according to the IEEE 754 standard.

Original entry on oeis.org

170141183460469231731687303715884105728, 14348907, 85070591730234615865843651857942052864, 9765625, 470184984576, 5764801, 85070591730234615865843651857942052864, 4782969, 10000000000, 1771561, 15407021574586368, 4826809, 1475789056, 11390625, 21267647932558653966460912964485513216

Offset: 2

Hugo Pfoertner, Aug 04 2020

			a(3) = 14348907 = 3^15, because the next power 3^16 = 43046721 cannot be exactly represented as a binary32 floating point number, but only rounded to 43046720.

Hugo Pfoertner, Table of n, a(n) for n = 2..16384

Cf. A336774, A336778, A336779.

a(n) = n^(A336774(n)-1).

A336778 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 differs from the exact value n^a(n), when the multiplication is performed using 64-bit double precision floats according to the IEEE 754 standard.

Original entry on oeis.org

1024, 34, 512, 23, 34, 19, 342, 17, 23, 16, 34, 15, 19, 14, 256, 13, 17, 13, 23, 13, 16, 12, 34, 12, 15, 12, 19, 11, 14, 11, 205, 11, 13, 11, 17, 11, 13, 11, 23, 10, 13, 10, 16, 10, 12, 10, 34, 10, 12, 10, 15, 10, 12, 10, 19, 10, 11, 10, 14, 9, 11, 9, 171, 9, 11

Offset: 2

Hugo Pfoertner, Aug 04 2020

See A336774 for more information and links.

For n a power of two the first deviation is caused by exceeding the maximum representable number of the binary64 double precision floating point format with result +infinity in standard conforming implementations.

Hugo Pfoertner, Table of n, a(n) for n = 2..1600
Hugo Pfoertner, Comparison with exact results, range n=2..128, computed on x86-64 architecture.

Cf. A336774, A336775, A336776, A336779, A336780.

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.

Original entry on oeis.org

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.

A336781 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 64-bit double precision floats according to the IEEE 754 standard.

Original entry on oeis.org

1076, 680, 539, 464, 417, 384, 360, 341, 325, 312, 301, 292, 284, 277, 270, 264, 259, 255, 250, 246, 243, 239, 236, 233, 230, 228, 225, 223, 221, 218, 216, 215, 213, 211, 209, 208, 206, 205, 203, 202, 201, 200, 198, 197, 196, 195, 194, 193, 192, 191, 190, 189, 188

Offset: 2

Hugo Pfoertner, Aug 07 2020

See A336777 and A336774 for more information and links.

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

Cf. A336774, A336775, A336776, A336777, A336778, A336779, A336780.

cp's OEIS Frontend

A336774 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 differs from the exact value n^a(n), when the multiplication is performed using 32-bit single precision floats according to the IEEE 754 standard.

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A336775 a(n) is the largest power of n such that all numbers n^k <= a(n), k=1,..,A336774(n)-1 can be exactly represented as single precision 32-bit floating point numbers according to the IEEE 754 standard.

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A336778 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 differs from the exact value n^a(n), when the multiplication is performed using 64-bit double precision floats according to the IEEE 754 standard.

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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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A336781 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 64-bit double precision floats according to the IEEE 754 standard.

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