A282115 Numbers m with k digits in base b (MSD(m)=d_k, LSD(m)=d_1) such that, for one of their digits in position d_k < j < d_1, Sum_{i=j+1..k} (i-j)*d_i = Sum_{i=1..j-1} (j-i)*d_i. Case b = 10.

101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 404, 414, 424, 434, 444, 454, 464, 474, 484, 494, 505, 515, 525, 535, 545, 555, 565, 575, 585, 595, 606, 616, 626

Offset

1,1

Comments

All the numbers that are palindromic in base 10 and have an odd number of digits belong to this sequence.

Here the fulcrum is one of the digits while in the sequences from A282143 to A282151 it is between two digits.

Links

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

Example

10467: if j = 2 (digit 6) we have 4*1 + 0*2 + 1*3 = 7 for the left side and 7*1 = 7 for the right side.

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), 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, A282108, A282109, A282110, A282111, A282112, A282113, A282114.

Sequence in context: A303571 A303573 A050661 * A116642 A283590 A279173

Adjacent sequences: A282112 A282113 A282114 * A282116 A282117 A282118

Keyword

nonn,base,easy

Author

Paolo P. Lava, Feb 06 2017

Status

approved