A282151 - OEIS

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.

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

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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):