A345442 Denominators of irregular triangle of fractions arising from a problem of projecting into Hilbert space.

1, 2, 1, 4, 4, 8, 1, 16, 8, 8, 32, 16, 16, 1, 64, 32, 16, 16, 128, 64, 64, 32, 1, 256, 128, 32, 32, 64, 32, 512, 256, 256, 128, 128, 1, 1024, 512, 256, 16, 64, 128, 64, 2048, 1024, 1024, 512, 128, 256, 256, 1, 4096, 2048, 128, 512, 1024, 256, 128, 128, 8192, 4096, 4096, 2048, 2048, 512, 512, 512

Offset

1,2

Links

Table of n, a(n) for n=1..66.

H. H. Bauschke and R. M. Corless, Analyzing a Projection Method with Maple, MapleTech Journal, 4:1 (1997), 2-7.

Example

Triangle begins:
[0],
[1/2],
[0,1/4],
[1/4,1/8],
[0,3/16,1/8],
[1/8,3/32,1/16,1/16],
[0,7/64,5/32,1/16],
[1/16,7/128,5/64,7/64,1/32],
[0,15/256,17/128,3/32,1/32,1/64],
[1/32,15/512,17/256,29/256,9/128,3/128],
[0,31/1024,49/512,23/256,1/16,3/64,1/128],
...

Prog

(PARI) tabfd(nn) = my(m = htabl(nn), v = vector(nn, n, apply(denominator, Vec(m[n, ], len(m[n, ], n))))); for (n=1, #v, for (k=1, #v[n], print1(v[n][k], ", "))); \\ uses htabl and len from A345441 \\ Michel Marcus, Mar 20 2023

Crossrefs

Cf. A345441 (numerators).

Sequence in context: A077967 A296188 A008312 * A060723 A300622 A195691

Adjacent sequences: A345439 A345440 A345441 * A345443 A345444 A345445

Keyword

nonn,frac,tabf

Author

N. J. A. Sloane, Jun 27 2021

Extensions

More terms from Michel Marcus, Mar 20 2023

Status

approved