A058084 Smallest m such that binomial(m,k) = n for some k.

0, 2, 3, 4, 5, 4, 7, 8, 9, 5, 11, 12, 13, 14, 6, 16, 17, 18, 19, 6, 7, 22, 23, 24, 25, 26, 27, 8, 29, 30, 31, 32, 33, 34, 7, 9, 37, 38, 39, 40, 41, 42, 43, 44, 10, 46, 47, 48, 49, 50, 51, 52, 53, 54, 11, 8, 57, 58, 59, 60, 61, 62, 63, 64, 65, 12, 67, 68, 69, 8, 71, 72, 73, 74, 75, 76

Offset

1,2

Comments

Index of first row of Pascal's triangle (A007318) containing n.

Links

Pontus von Brömssen, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe, with 3 corrections).

Formula

a(A006987(n)) < A006987(n); a(A137905(n)) = A137905(n). - Reinhard Zumkeller, Mar 20 2009

A007318(a(n), A357327(n)) = n. - Pontus von Brömssen, Sep 24 2022

Example

a(28)=8 because 28 is first found in row 8 of Pascal's triangle (where the first row is counted as 0).

Maple

with(combinat): for n from 2 to 150 do flag := 0: for m from 1 to 150 do for k from 1 to m do if binomial(m, k) = n then printf(`%d, `, m); flag := 1; break fi: od: if flag=1 then break fi; od: od:

Mathematica

nmax = 76; t = Table[Binomial[m, k], {m, 0, nmax}, {k, 0, m}]; a[n_] := Position[t, n, 2, 1][[1, 1]]-1; Table[a[n], {n, 1, nmax}] (* Jean-François Alcover, Nov 30 2011 *)

Prog

(Haskell)
import Data.List (findIndex); import Data.Maybe (fromJust)
a058084 n = fromJust $ findIndex (elem n) a007318_tabl
-- Reinhard Zumkeller, Nov 09 2011
(PARI) a(n) = my(k=0); while (!vecsearch(vector((k+2)\2, i, binomial(k, i-1)), n), k++); k; \\ Michel Marcus, Dec 07 2021

Crossrefs

Cf. A007318, A006987, A137905, A357327.

Sequence in context: A130065 A079881 A349958 * A074882 A273284 A079867

Adjacent sequences: A058081 A058082 A058083 * A058085 A058086 A058087

Keyword

nice,nonn,easy

Author

Fabian Rothelius, Nov 25 2000

Extensions

More terms from James A. Sellers, Nov 27 2000

Status

approved