A139128 Number of distinct representations A005244(n) = A005244(i)*A005244(j)-1 with i < j.

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, 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, 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

Offset

1,28

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000 (n = 1 to 500 from R. Zumkeller)

Eric Weisstein's World of Mathematics, Hofstadter Sequences

Index entries for Hofstadter-type sequences

Example

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

Maple

R:= [2, 3]: count:= 2:
for i from 4 while count < 10000 do
  found:= false;
  for j from 1 while R[j]^2 < i+1 do
    if i mod R[j] = R[j]-1 and ListTools:-BinarySearch(R, (i+1)/R[j]) <> 0 then
      found:= true; break
    fi
  od;
  if found then R:= [op(R), i]; count:= count+1;
od:
f:= proc(n) local t, i, j, x, L;
  x:= R[n]+1:
  L:= R[1..n-1];
  t:= 0:
  for i from 1 while R[i]^2 < x do
    if x mod R[i] = 0 and ListTools:-BinarySearch(L, x/R[i]) <> 0 then t:= t+1 fi
  od;
  t
end proc:
map(f, [$1..10000]); # Robert Israel, Jun 21 2024

Crossrefs

Sequence in context: A128184 A373244 A025450 * A106752 A136441 A030561

Adjacent sequences: A139125 A139126 A139127 * A139129 A139130 A139131

Keyword

nonn

Author

Reinhard Zumkeller, Apr 09 2008

Extensions

a(2) corrected and definition clarified by Robert Israel, Jun 21 2024

Status

approved