A139128 - OEIS

%I #18 Jun 22 2024 08:01:55

%S 0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,1,

%T 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,1,1,1,1,1,1,1,1,2,1,1,1,

%U 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,3

%N Number of distinct representations A005244(n) = A005244(i)*A005244(j)-1 with i < j.

%C A139129 gives the smallest terms in A005244 having exactly n representations.

%H Robert Israel, <a href="/A139128/b139128.txt">Table of n, a(n) for n = 1..10000</a> (n = 1 to 500 from R. Zumkeller)

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HofstadterSequences.html">Hofstadter Sequences</a>

%H <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>

%e A005244(28) = 129: a(28) = #{26*5-1,65*2-1} = 2.

%p R:= [2,3]: count:= 2:

%p for i from 4 while count < 10000 do

%p   found:= false;

%p   for j from 1 while R[j]^2 < i+1 do

%p     if i mod R[j] = R[j]-1 and ListTools:-BinarySearch(R,(i+1)/R[j]) <> 0 then

%p       found:= true; break

%p     fi

%p   od;

%p   if found then R:= [op(R),i]; count:= count+1;

%p od:

%p f:= proc(n) local t,i,j,x,L;

%p   x:= R[n]+1:

%p   L:= R[1..n-1];

%p   t:= 0:

%p   for i from 1 while R[i]^2 < x do

%p     if x mod R[i] = 0 and ListTools:-BinarySearch(L,x/R[i]) <> 0 then t:= t+1 fi

%p   od;

%p   t

%p end proc:

%p map(f, [$1..10000]); # _Robert Israel_, Jun 21 2024

%K nonn

%O 1,28

%A _Reinhard Zumkeller_, Apr 09 2008

%E a(2) corrected and definition clarified by _Robert Israel_, Jun 21 2024