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A282149 Numbers n with k digits in base x (MSD(n)=d_k, LSD(n)=d_1) such that, chosen one of their digits in position d_k < j < d_1, is Sum_{i=j..k}{(i-j+1)*d_i} = Sum_{i=1..j-1}{(j-i)*d_i}. Case x = 8. 2
9, 18, 27, 36, 45, 54, 63, 66, 72, 75, 84, 93, 102, 111, 129, 132, 141, 144, 150, 159, 198, 201, 207, 216, 258, 273, 288, 330, 345, 360, 387, 402, 417, 432, 459, 474, 489, 504, 513, 515, 524, 528, 533, 542, 551, 576, 581, 585, 590, 599, 600, 642, 647, 657, 672 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All the palindromic numbers in base 8 with an even number of digits belong to the sequence.

Here the fulcrum is between two digits while in the sequence from A282107 to A282115 is one of the digits.

The first number with this property in all the bases from 2 to 8 is

10296444436. - Giovanni Resta, Feb 16 2017

LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..10000

EXAMPLE

672 in base 8 is 1240. If we split the number in 12 and 40 we have 2*1 + 1*2 = 4 for the left side and 4*1 + 0*2 = 4 for the right one.

MAPLE

with(numtheory): P:=proc(q, h) local a, b, d, j, k, n, s;

for n from 1 to q do a:=convert(n, base, h);

for k from 1 to trunc(nops(a)/2) do b:=a[k]; a[k]:=a[nops(a)-k+1]; a[nops(a)-k+1]:=b; od;

for k from 1 to nops(a)-1 do d:=0; s:=0;

for j from 1 to k do if a[j]>0 then s:=s+a[j]*(k-j+1); fi; od; for j from nops(a) by -1 to k+1 do

if a[j]>0 then d:=d+a[j]*(j-k); fi; od; if d=s then print(n); break; fi; od; od; end: P(10^3, 8);

CROSSREFS

Cf. A282107 - A282115, A282143 - A282148, A282150, A282151.

Sequence in context: A119310 A037993 A044849 * A114612 A108782 A178734

Adjacent sequences:  A282146 A282147 A282148 * A282150 A282151 A282152

KEYWORD

nonn,base,easy

AUTHOR

Paolo P. Lava, Feb 15 2017

STATUS

approved

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Last modified December 11 05:41 EST 2017. Contains 295868 sequences.