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A282151 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 = 10. 17
11, 22, 33, 44, 55, 66, 77, 88, 99, 102, 110, 113, 124, 135, 146, 157, 168, 179, 201, 204, 215, 220, 226, 237, 248, 259, 306, 311, 317, 328, 330, 339, 402, 408, 419, 421, 440, 512, 531, 550, 603, 622, 641, 660, 713, 732, 751, 770, 804, 823, 842, 861, 880, 914, 933 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All the palindromic numbers in base 10 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.

LINKS

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

EXAMPLE

If we split 2039 in 203 and 9 we have 3*1 + 0*2 + 2*3 = 9 for the left side and 9*1 = 9 for the right one.

MAPLE

P:=proc(n, h) local a, j, k: a:=convert(n, base, h):

for k from 1 to nops(a)-1 do

if add(a[j]*(k-j+1), j=1..k)=add(a[j]*(j-k), j=k+1..nops(a))

then RETURN(n); break: fi: od: end: seq(P(i, 10), i=1..10^3);

CROSSREFS

Cf. A282107 - A282115, A282143 - A282150.

Sequence in context: A108203 A308104 A108773 * A333614 A109052 A178358

Adjacent sequences:  A282148 A282149 A282150 * A282152 A282153 A282154

KEYWORD

nonn,base,easy

AUTHOR

Paolo P. Lava, Feb 15 2017

STATUS

approved

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Last modified August 7 19:57 EDT 2020. Contains 336279 sequences. (Running on oeis4.)