A163598 The smallest triangular number that contains the digits of n in its exact middle.

1, 120, 3, 741, 153, 6, 171, 780, 190, 10, 111156, 1128, 131328, 2145, 15, 3160, 1176, 4186, 101926, 152076, 21, 1225, 102378, 3240, 5253, 7260, 1275, 28, 232903, 113050, 9316, 1326, 133386, 2346, 5356, 36, 1378, 7381, 133903, 3403, 2415, 124251, 1431

Offset

1,2

Comments

"Exact middle" means that the counts of digits of the triangular number to the left and to the right of the digits of n are the same.

Leading 0's are not allowed, e.g. 30135 is not considered to have the digits of 13 in its exact middle. - Robert Israel, Nov 22 2017

Essentially the same as A062690. - Georg Fischer, Oct 01 2018

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(22) = 1225 = 1//22//5 = A000217(49) is the smallest member of A000217 which displays 22 in the middle. - R. J. Mathar, Aug 11 2009

Maple

N:= 100: # to get a(1)..a(N)
Mid:= proc(t, d, i)
   local s;
   if d::odd then
      s:= floor(t/10^((d+1)/2-i)) mod 10^(2*i-1);
      if ilog10(s) < 2*i-2 then s:= NULL fi
   else s:= floor(t/10^(d/2-i)) mod 10^(2*i);
      if ilog10(s) < 2*i-1 then s:= NULL fi
   fi;
   s
end proc:
V:= Vector(N):
count:= 0:
for k from 1 while count < N do
  t:= k*(k+1)/2;
  d:= ilog10(t)+1;
  L:= [seq(Mid(t, d, i), i=1..(d+(d mod 2))/2)];
  for x in L do
    if x <= N and x > 0 and V[x] = 0 then
      count:= count+1;
      V[x]:= t;
    fi
   od
od:
convert(V, list); # Robert Israel, Nov 22 2017

Crossrefs

Sequence in context: A267570 A267286 A062829 * A062690 A267745 A267025

Adjacent sequences: A163595 A163596 A163597 * A163599 A163600 A163601

Keyword

nonn,base,look

Author

Claudio Meller, Aug 01 2009

Extensions

a(20) corrected by Robert Israel, Nov 22 2017

Status

approved