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A163598 The smallest triangular number that contains the digits of n in its exact middle. 1


%S 1,120,3,741,153,6,171,780,190,10,111156,1128,131328,2145,15,3160,

%T 1176,4186,101926,152076,21,1225,102378,3240,5253,7260,1275,28,232903,

%U 113050,9316,1326,133386,2346,5356,36,1378,7381,133903,3403,2415,124251,1431

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

%C "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.

%C 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

%C Essentially the same as A062690. - _Georg Fischer_, Oct 01 2018

%H Robert Israel, <a href="/A163598/b163598.txt">Table of n, a(n) for n = 1..10000</a>

%e 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

%p N:= 100: # to get a(1)..a(N)

%p Mid:= proc(t,d,i)

%p local s;

%p if d::odd then

%p s:= floor(t/10^((d+1)/2-i)) mod 10^(2*i-1);

%p if ilog10(s) < 2*i-2 then s:= NULL fi

%p else s:= floor(t/10^(d/2-i)) mod 10^(2*i);

%p if ilog10(s) < 2*i-1 then s:= NULL fi

%p fi;

%p s

%p end proc:

%p V:= Vector(N):

%p count:= 0:

%p for k from 1 while count < N do

%p t:= k*(k+1)/2;

%p d:= ilog10(t)+1;

%p L:= [seq(Mid(t,d,i),i=1..(d+(d mod 2))/2)];

%p for x in L do

%p if x <= N and x > 0 and V[x] = 0 then

%p count:= count+1;

%p V[x]:= t;

%p fi

%p od

%p od:

%p convert(V,list); # _Robert Israel_, Nov 22 2017

%K nonn,base,look

%O 1,2

%A _Claudio Meller_, Aug 01 2009

%E a(20) corrected by _Robert Israel_, Nov 22 2017

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Last modified August 13 08:18 EDT 2022. Contains 356079 sequences. (Running on oeis4.)