SloaneA

The $n$-th term of an OEIS sequence, id a quoted A-number — scoped to the specific sequences Fungrim's own SloaneA identities cite, each aliased to a head that already computes it. Provided by @enumeratio/analytic.

✓ checked against that system · ! checked, with disagreements (hover a chip)FungrimSloaneA✓↗Fungrim entry

SloaneA(id, n)the $n$-th term of OEIS sequence id.

Typed signatures

Type	Package	Applies
(string, integer) -> number	analytic	always

Domain: Special functions

Details

• A general OEIS lookup is out of reach — most sequences have no closed form at all — so this aliases exactly the A-numbers Fungrim's identities use: A000045 (Fibonacci), A000040 (the primes, via PrimeNumber), A000720 (PrimePi), A000041 (NPartition), A000110 (BellNumber), A000142 (Factorial), A027641/A027642 (the numerator/denominator of BernoulliB), and A000793 (Landau's function $g(n)$, the largest order of an element of $S_n$ — computed directly, since compute-engine's LandauG is a symbolic stub with no numeric evaluator).
• An id this package does not carry stays symbolic rather than guessing (e.g. A060691, which Fungrim cites only inside a derivative formula for AGM's Taylor coefficients, not as an equation for the sequence's value).

Plot

argument id of type string has no control

Examples

Basic #

A000045 is the Fibonacci numbers: the 10th is 55

live ↗

In$\mathrm{SloaneA}(\text{A000045}, 10)$Out$55$

A000793, Landau's function: $g(10) = 30$

live ↗

In$\mathrm{SloaneA}(\text{A000793}, 10)$Out$30$

Scope #

1 / 6

A000040(5) = 11, the 5th prime.

live ↗

In$\mathrm{SloaneA}(\text{A000040}, 5)$Out$11$

1 / 2

A027641(12) = −691, $B_{12}$'s numerator.

live ↗

In$\mathrm{SloaneA}(\text{A027641}, 12)$Out$-691$

Possible issues #

An OEIS id outside the declared alias table stays symbolic

live ↗

In$\mathrm{SloaneA}(\text{A060691}, 5)$Out$\mathrm{SloaneA}(\text{A060691}, 5)$

About

Examples	11
Checked against	Wolfram Language 10 agree1 differ
Crosswalk	FungrimFungrim entry ×9

Implementation

primitive · numericirreducibly numeric — it evaluates rather than rewrites

nativeenginetypescriptpackages/symbols/analysis/analytic/src/sloane-a.ts

mappedwolframpackages/oracle/src/mappings.ts

No built-in OEIS-by-id lookup, but the Function Repository's OEISSequence/OEISSequenceData, read against each sequence's own OEIS offset, lands on the n-th term uniformly across every id this head aliases -- matches all seven (A000045/10 = 55, A000793/10 = 30, A000040/5 = 11, A000041/10 = 42, A000110/5 = 52, A000142/5 = 120, A000720/20 = 8). Needs network access to the Function Repository (and, transitively, oeis.org) to run. A060691, outside this head's alias table and left symbolic on our side, disagrees once the scan runs -- that is a scope difference (we don't claim that id), not a wrong answer.

See also: Fibonacci, BellNumber, BernoulliB