Ulam sequence
E85412
The Ulam sequence is an integer sequence starting with 1 and 2 in which each subsequent term is the smallest integer that can be written uniquely as the sum of two distinct earlier terms.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Ulam sequence canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T718423 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Ulam sequence Context triple: [Stanislaw Ulam, notableWork, Ulam sequence]
-
A.
Look-and-say sequence
The look-and-say sequence is a famous integer sequence where each term is generated by verbally describing the digits of the previous term, studied for its surprising combinatorial and growth properties.
-
B.
Fibonacci sequence
The Fibonacci sequence is an infinite series of numbers where each term is the sum of the two preceding ones, widely used in mathematics, art, and design due to its connection with the golden ratio and natural growth patterns.
-
C.
Dyson’s transform in number theory
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
-
D.
Surreal numbers
Surreal numbers are a class of numbers introduced by John H. Conway that form an extensive ordered field encompassing the real numbers, infinite quantities, and infinitesimals within a unified framework.
-
E.
Gauss’s constant
Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Ulam sequence Target entity description: The Ulam sequence is an integer sequence starting with 1 and 2 in which each subsequent term is the smallest integer that can be written uniquely as the sum of two distinct earlier terms.
-
A.
Look-and-say sequence
The look-and-say sequence is a famous integer sequence where each term is generated by verbally describing the digits of the previous term, studied for its surprising combinatorial and growth properties.
-
B.
Fibonacci sequence
The Fibonacci sequence is an infinite series of numbers where each term is the sum of the two preceding ones, widely used in mathematics, art, and design due to its connection with the golden ratio and natural growth patterns.
-
C.
Dyson’s transform in number theory
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
-
D.
Surreal numbers
Surreal numbers are a class of numbers introduced by John H. Conway that form an extensive ordered field encompassing the real numbers, infinite quantities, and infinitesimals within a unified framework.
-
E.
Gauss’s constant
Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
- F. None of above. chosen
Statements (59)
| Predicate | Object |
|---|---|
| instanceOf |
integer sequence
ⓘ
mathematical sequence ⓘ |
| definedByRecurrence | Each subsequent term is the smallest integer that can be written uniquely as the sum of two distinct earlier terms ⓘ |
| field | number theory ⓘ |
| firstFewTerms |
1
ⓘ
102 ⓘ 106 ⓘ 11 ⓘ 114 ⓘ 128 ⓘ 13 ⓘ 131 ⓘ 138 ⓘ 139 ⓘ 148 ⓘ 155 ⓘ 156 ⓘ 16 ⓘ 166 ⓘ 177 ⓘ 18 ⓘ 180 ⓘ 189 ⓘ 2 ⓘ 26 ⓘ 28 ⓘ 3 ⓘ 36 ⓘ 38 ⓘ 4 ⓘ 47 ⓘ 48 ⓘ 53 ⓘ 57 ⓘ 6 ⓘ 62 ⓘ 69 ⓘ 71 ⓘ 78 ⓘ 8 ⓘ 81 ⓘ 85 ⓘ 97 ⓘ 99 ⓘ |
| hasFirstTerm | 1 ⓘ |
| hasOEISID | A002858 ⓘ |
| hasOpenProblems | true ⓘ |
| hasSecondTerm | 2 ⓘ |
| hasSummandConstraint | summands must be distinct earlier terms ⓘ |
| hasUniquenessConstraint | sum representation must be unique ⓘ |
| isDeterministic | true ⓘ |
| isInfinite | true ⓘ |
| isNonPeriodic | true ⓘ |
| isStrictlyIncreasing | true ⓘ |
| namedAfter |
Stanislaw Ulam
ⓘ
surface form:
Stanisław Ulam
|
| requiresDistinctSummands | true ⓘ |
| requiresUniqueRepresentationAsSum | true ⓘ |
| startTermsFixed | 1 and 2 ⓘ |
| usesOperation | addition ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Ulam sequence Description of subject: The Ulam sequence is an integer sequence starting with 1 and 2 in which each subsequent term is the smallest integer that can be written uniquely as the sum of two distinct earlier terms.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.