cp's OEIS Frontend

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.

%I A053405 #20 Jul 02 2025 16:01:59
%S A053405 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,
%T A053405 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,
%U A053405 12,12,11,11,11,11,10,10,12,12,12,12,12,11,11,11,10,13,13,13,12,12,12,12
%N 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.
%H A053405 Reinhard Zumkeller, <a href="/A053405/b053405.txt">Table of n, a(n) for n = 4..10000</a>
%F A053405 a(n) = A257213(n-1) + 1. - _Ridouane Oudra_, Apr 19 2025
%e A053405 7 kara 4 = 2 because 2 * 4 > 7 and 2 * 3 < 7.
%e A053405 7 kara 5 is undefined: 7 kara 5 != 2 because 2 * (5-1) > 7 and 7 kara 5 != 1 because 1 * 5 < 7.
%e A053405 4 kara 3 is undefined: 4 kara 2 = 2; 4 kara 4 = 1.
%t A053405 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 *)
%o A053405 (Haskell)
%o A053405 a053405 n = head [a | a <- [1..], n `kara` a == Nothing] where
%o A053405    kara a b = if null ks then Nothing else Just $ head ks
%o A053405               where ks = [c | c <- [1..a], a <= c * b, a > c * (b - 1)]
%o A053405 -- _Reinhard Zumkeller_, Mar 30 2013
%Y A053405 Cf. A053087, A257213.
%K A053405 nice,nonn,easy
%O A053405 4,1
%A A053405 Robert Lozyniak (11(AT)onna.com), Jan 08 2000
%E A053405 Corrected and extended by _James Sellers_, Jan 10 2000