A053405 Definition: A kara B = C, where C is the least nonnegative integer such that C * B >= A and C * (B-1) < A. a(n) is the smallest k such that n kara k is undefined.

3, 4, 4, 5, 5, 4, 6, 5, 5, 6, 6, 6, 5, 7, 7, 6, 6, 8, 7, 7, 7, 6, 8, 8, 8, 7, 7, 9, 9, 8, 8, 8, 7, 9, 9, 9, 9, 8, 8, 10, 10, 10, 9, 9, 9, 8, 11, 10, 10, 10, 10, 9, 9, 11, 11, 11, 11, 10, 10, 10, 9, 12, 12, 11, 11, 11, 11, 10, 10, 12, 12, 12, 12, 12, 11, 11, 11, 10, 13, 13, 13, 12, 12, 12, 12

Offset

4,1

Links

Reinhard Zumkeller, Table of n, a(n) for n = 4..10000

Example

7 kara 4 = 2 because 2 * 4 > 7 and 2 * 3 < 7.
7 kara 5 is undefined: 7 kara 5 != 2 because 2 * (5-1) > 7 and 7 kara 5 != 1 because 1 * 5 < 7.
4 kara 3 is undefined: 4 kara 2 = 2; 4 kara 4 = 1.

Mathematica

kara[a_, b_] := Module[{r, c}, r = Reduce[c*b >= a && c*(b-1) < a, c, Integers]; If[r === False, Null, c /. {ToRules[r]} // First]]; a[n_] := For[k = 2, True, k++, If[!IntegerQ[n ~kara~ k], Return[k]]]; Table[a[n], {n, 4, 88}] (* Jean-François Alcover, Sep 13 2013 *)

Prog

(Haskell)
a053405 n = head [a | a <- [1..], n `kara` a == Nothing] where
   kara a b = if null ks then Nothing else Just $ head ks
              where ks = [c | c <- [1..a], a <= c * b, a > c * (b - 1)]
-- Reinhard Zumkeller, Mar 30 2013

Crossrefs

Cf. A053087.

Sequence in context: A107574 A341730 A241163 * A133196 A179841 A059183

Adjacent sequences: A053402 A053403 A053404 * A053406 A053407 A053408

Keyword

nice,nonn,easy

Author

Robert Lozyniak (11(AT)onna.com), Jan 08 2000

Extensions

Corrected and extended by James A. Sellers, Jan 10 2000

Status

approved