SHMARQL

Collatz conjecture

<http://www.wikidata.org/entity/Q837314>

conjecture in mathematics that concerns sequences
Collatz conjecture
Collatz conjecture
rdfs:label
"Collatz conjecture"@en
skos:altLabel
"3n+1 conjecture"@en
"3x+1 problem"@en
"Hailstone problem"@en
"Hasse's algorithm"@en
"Kakutani's problem"@en
"Syracuse problem"@en
"Thwaites conjecture"@en
"Ulam conjecture"@en
schema:description
"conjecture in mathematics that concerns sequences"@en
schema:dateModified "2026-09-27T16:19:12+00:00"^^xsd:dateTime
schema:version 2550089116
wikibase:identifiers 14
wikibase:sitelinks 43
wikibase:statements 32
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p:P12800 wd:statement/Q837314-D1A8111D-1AA1-40F5-82E0-80BE63960633
p:P12975 wd:statement/Q837314-c351e01f-3de5-4341-ab06-b3c2940799e9
p:P1343 wd:statement/Q837314-73220f25-4cfc-6243-ab24-138a1f53e908
p:P13772 wd:statement/Q837314-2647A9E6-1B52-43C4-8066-0085A61FC2DB
p:P138 wd:statement/Q837314-19a19e53-42fa-8cd0-cfbc-7bf5f4792c34
wd:statement/Q837314-2616f955-449c-4658-7f31-fccb7ade6d62
wd:statement/Q837314-2e7a9872-4628-e0f1-af1d-da7ffd09435b
wd:statement/Q837314-4621f4cb-4706-3e95-1ccb-55947e6f1cad
wd:statement/q837314-8E63736C-CA10-490C-81BC-8D7DC9B04148
p:P18 wd:statement/Q837314-054360fc-400b-eba3-2af9-3744eea1e182
wd:statement/Q837314-eb519834-4778-e4a5-9e2b-cee3a4ee401a
p:P227 wd:statement/Q837314-56D8FD68-D894-4974-8E01-73706AE28F90
p:P2534 wd:statement/Q837314-9ebb65fd-4387-deb3-1a65-695feb7b1496
p:P2812 wd:statement/Q837314-4D036592-5E0C-41F7-8637-2C95D96072D9
p:P31 wd:statement/Q837314-75a71c61-48cf-12c0-bc83-d6003da7a43a
p:P3417 wd:statement/Q837314-9020DC94-A7F9-40E6-90AD-3D1E984EF870
p:P361 wd:statement/Q837314-3977f045-4b1b-f56e-128a-1189983dec4d
wd:statement/Q837314-f015bff8-4a97-14db-e6a8-e55f2a5253a8
p:P373 wd:statement/Q837314-7510DCA8-88D1-42D5-9674-62A3C3E7D2C0
p:P5106 wd:statement/Q837314-0930E8E2-E343-48F2-9B91-2005C78FB464
p:P577 wd:statement/Q837314-fb0ecd7d-463e-2bc2-e0b9-477029b90377
p:P61 wd:statement/Q837314-077f64f0-46d4-75f4-eab8-9f8a8474e505
p:P6104 wd:statement/Q837314-B4073D4F-79CB-4DBE-B712-90E538CDEF0D
p:P6366 wd:statement/Q837314-E3B686E1-5DD1-4D51-B87B-462DCBDF34B2
p:P646 wd:statement/Q837314-BEC5CA02-0D29-479E-86DA-30E263EC3A2D
p:P6781 wd:statement/Q837314-f18fcdb2-4436-1298-bd5a-c125aff25a53
p:P6900 wd:statement/Q837314-bf93c331-4e17-9c26-80ea-190adf0da5a4
p:P8885 wd:statement/Q837314-5abcfd52-431a-ef46-fe18-871b7bc2a526
p:P921 wd:statement/Q837314-23a59f32-45d4-dfc1-8463-23823cd94dc2
p:P9621 wd:statement/Q837314-b721a02b-4fe1-7b16-a421-c22f9b92accb
p:direct-normalized/P227 <https://d-nb.info/gnd/4768879-8>
p:direct-normalized/P6366 <https://makg.org/entity/128814272>
wdt:P10283 "C128814272"
wdt:P1269 arithmetic dynamics
wdt:P12800 "fr:Conjecture_de_Syracuse"
wdt:P12975 "1712"
wdt:P1343 On-Line Encyclopedia of Integer Sequences wiki
wdt:P13772 "collatz-conjecture"
wdt:P138 Stanisław Ulam
hail
Syracuse University
Lothar Collatz
Shizuo Kakutani
wdt:P18 <http://commons.wikimedia.org/wiki/Special:FilePath/All%20Collatz%20sequences%20of%20a%20length%20inferior%20to%2020.svg>
<http://commons.wikimedia.org/wiki/Special:FilePath/Collatz-graph-all-30-no27-loop.svg>
wdt:P227 "4768879-8"
wdt:P2534 "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mi>f</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mo data-mjx-texclass="OPEN">{</mo><mtable columnspacing="1em" rowspacing="4pt" columnalign="left left"><mtr><mtd><mn>3</mn><mi>n</mi><mo stretchy="false">+</mo><mn>1</mn></mtd><mtd><mn>2</mn><mo stretchy="false">&#x2224;</mo><mi>n</mi></mtd></mtr><mtr><mtd><mi>n</mi><mo lspace="0" rspace="0">/</mo><mn>2</mn></mtd><mtd><mn>2</mn><mo stretchy="false">&#x2223;</mo><mi>n</mi></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true" data-mjx-texclass="CLOSE"></mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi mathvariant="normal">&#x2200;</mi><mi>n</mi><mo stretchy="false">&#x2208;</mo><msup><mrow data-mjx-texclass="ORD"><mi>ℤ</mi></mrow><mrow data-mjx-texclass="ORD"><mo stretchy="false">+</mo></mrow></msup><mi mathvariant="normal">&#x2203;</mi><mi>i</mi><mo stretchy="false">&#x2208;</mo><mrow data-mjx-texclass="ORD"><mi>ℕ</mi></mrow><mo stretchy="false">&#x003A;</mo><mo stretchy="false">(</mo><munder><mrow data-mjx-texclass="OP"><munder><mrow data-mjx-texclass="ORD"><mi>f</mi><mo stretchy="false">&#x2218;</mo><mi>f</mi><mo stretchy="false">&#x2218;</mo><mo stretchy="false">&#x22EF;</mo><mo stretchy="false">&#x2218;</mo><mi>f</mi></mrow><mo>&#x23DF;</mo></munder></mrow><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></munder><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mn>1</mn></mtd></mtr></mtable></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
wdt:P2812 "CollatzProblem"
wdt:P31 conjecture
wdt:P3417 "Collatz-Conjecture"
wdt:P361 Unsolved Problems in Number Theory
list of unsolved problems in mathematics
wdt:P373 "Collatz conjecture"
wdt:P5106 "CollatzProblem"
wdt:P577 "1937-01-01T00:00:00+00:00"^^xsd:dateTime
wdt:P61 Lothar Collatz
wdt:P6104 WikiProject Mathematics
wdt:P6366 "128814272"
wdt:P646 "/m/09g1c"
wdt:P6781 "Collatz_Conjecture"
wdt:P6900 "コラッツの問題"
wdt:P8885 "콜라츠 추측"
wdt:P921 Collatz sequence
wdt:P9621 "congettura-di-collatz"
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