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
Examples
a(28)=8 because 28 is first found in row 8 of Pascal's triangle (where the first row is counted as 0).
Links
- Pontus von Brömssen, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe, with 3 corrections).
Programs
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Haskell
import Data.List (findIndex); import Data.Maybe (fromJust) a058084 n = fromJust $ findIndex (elem n) a007318_tabl -- Reinhard Zumkeller, Nov 09 2011
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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:
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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 *) -
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
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Python
def A058084(n): if n == 1: return 0 c = [1] for m in range(n): d = [1] for i in range(m): a = c[i]+c[i+1] if a == n: return m+1 d.append(a) c = d+[1] # Chai Wah Wu, Aug 23 2025
Formula
Extensions
More terms from James Sellers, Nov 27 2000
Comments