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A163598 The smallest triangular number that contains the digits of n in its exact middle. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 26 01:42 EDT 2022. Contains 354870 sequences. (Running on oeis4.)