The On-Line Encyclopedia of Integer Sequences (OEIS)

Revisions by Martin Renner (See also Martin Renner's wiki page)

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A376542

G.f.: Sum_{k>=0} x^(k^2) * Product_{j=1..k} (1 + x^(2*j))^2.
(history; published version)

#3 by Martin Renner at Thu Sep 26 17:35:44 EDT 2024

STATUS

editing

proposed

A376541

Natural numbers whose iterated squaring modulo 1000 eventually enters the 4-cycle 201, 401, 801, 601.
(history; published version)

#4 by Martin Renner at Thu Sep 26 17:33:57 EDT 2024

STATUS

editing

proposed

A376540

Natural numbers whose iterated squaring modulo 1000 eventually enters the 4-cycle 176, 976, 576, 776.
(history; published version)

#4 by Martin Renner at Thu Sep 26 17:33:45 EDT 2024

STATUS

editing

proposed

A376539

Natural numbers whose iterated squaring modulo 1000 eventually settles at the attractor 376.
(history; published version)

#5 by Martin Renner at Thu Sep 26 17:33:23 EDT 2024

STATUS

editing

proposed

A376538

Natural numbers whose iterated squaring modulo 1000 eventually settles at the attractor 1.
(history; published version)

#5 by Martin Renner at Thu Sep 26 17:33:10 EDT 2024

STATUS

editing

proposed

A376543

Numbers of the form p^e * q^f with p, q distinct primes = 3 mod 4 and e and f both odd.
(history; published version)

#2 by Martin Renner at Thu Sep 26 17:32:00 EDT 2024

NAME

allocated for Martin Renner

KEYWORD

allocated

recycled

A376541

Natural numbers whose iterated squaring modulo 1000 eventually enters the 4-cycle 201, 401, 801, 601.
(history; published version)

#3 by Martin Renner at Thu Sep 26 17:26:05 EDT 2024

COMMENTS

The natural numbers decompose into eight categories under the operation of repeated squaring modulo 1000, four of which consist of numbers that eventually settle at the attractors 0 (cf. A008592), 1 (cf. A376538), 376 (cf. A376539), or 625 (cf. A017329), two of which eventually enter one of the 4-cycles 176, 976, 576, 776 (cf. A376540) or 201, 401, 801, 601 (this sequence), and two of which eventually enter one of the 20-cycles 16, 256, 536, 296, 616, 456, 936, 96, 216, 656, 336, 896, 816, 856, 736, 696, 416, 56, 136, 496 (cf. A376542A376508) or 41, 681, 761, 121, 641, 881, 161, 921, 241, 81, 561, 721, 841, 281, 961, 521, 441, 481, 361, 321 (cf. A376543A376509).

CROSSREFS

Cf. A008592, A017329, A376506, A376507, A376508, A376509, A376538, A376539, A376540, A376542, A376543.

A376540

Natural numbers whose iterated squaring modulo 1000 eventually enters the 4-cycle 176, 976, 576, 776.
(history; published version)

#3 by Martin Renner at Thu Sep 26 17:24:56 EDT 2024

COMMENTS

The natural numbers decompose into eight categories under the operation of repeated squaring modulo 1000, four of which consist of numbers that eventually settle at the attractors 0 (cf. A008592), 1 (cf. A376538), 376 (cf. A376539), or 625 (cf. A017329), two of which eventually enter one of the 4-cycles 176, 976, 576, 776 (this sequence) or 201, 401, 801, 601 (cf. A376541), and two of which eventually enter one of the 20-cycles 16, 256, 536, 296, 616, 456, 936, 96, 216, 656, 336, 896, 816, 856, 736, 696, 416, 56, 136, 496 (cf. A376542A376508) or 41, 681, 761, 121, 641, 881, 161, 921, 241, 81, 561, 721, 841, 281, 961, 521, 441, 481, 361, 321 (cf. A376543A376509).

CROSSREFS

Cf. A008592, A017329, A376506, A376507, A376508, A376509, A376538, A376539, A376541, A376542, A376543.

A376539

Natural numbers whose iterated squaring modulo 1000 eventually settles at the attractor 376.
(history; published version)

#4 by Martin Renner at Thu Sep 26 17:23:36 EDT 2024

COMMENTS

The natural numbers decompose into eight categories under the operation of repeated squaring modulo 1000, four of which consist of numbers that eventually settle at the attractors 0 (cf. A008592), 1 (cf. A376538), 376 (this sequence), or 625 (cf. A017329), two of which eventually enter one of the 4-cycles 176, 976, 576, 776 (cf. A376540) or 201, 401, 801, 601 (cf. A376541), and two of which eventually enter one of the 20-cycles 16, 256, 536, 296, 616, 456, 936, 96, 216, 656, 336, 896, 816, 856, 736, 696, 416, 56, 136, 496 (cf. A376542A376508) or 41, 681, 761, 121, 641, 881, 161, 921, 241, 81, 561, 721, 841, 281, 961, 521, 441, 481, 361, 321 (cf. A376543A376509).

CROSSREFS

Cf. A008592, A017329, A376506, A376507, A376508, A376509, A376538, A376540, A376541, A376542, A376543.

A376538

Natural numbers whose iterated squaring modulo 1000 eventually settles at the attractor 1.
(history; published version)

#4 by Martin Renner at Thu Sep 26 17:22:30 EDT 2024

COMMENTS

The natural numbers decompose into eight categories under the operation of repeated squaring modulo 1000, four of which consist of numbers that eventually settle at the attractors 0 (cf. A008592), 1 (this sequence), 376 (cf. A376539), or 625 (cf. A017329), two of which eventually enter one of the 4-cycles 176, 976, 576, 776 (cf. A376540) or 201, 401, 801, 601 (cf. A376541), and two of which eventually enter one of the 20-cycles 16, 256, 536, 296, 616, 456, 936, 96, 216, 656, 336, 896, 816, 856, 736, 696, 416, 56, 136, 496 (cf. A376542A376508) or 41, 681, 761, 121, 641, 881, 161, 921, 241, 81, 561, 721, 841, 281, 961, 521, 441, 481, 361, 321 (cf. A376543A376509).

CROSSREFS

Cf. A008592, A017329, A376506, A376507, A376508, A376509, A376539, A376540, A376541, A376542, A376543.