A282150 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 = 9.

10, 20, 30, 40, 50, 60, 70, 80, 83, 90, 93, 103, 113, 123, 133, 143, 163, 166, 176, 180, 186, 196, 206, 249, 253, 259, 269, 270, 326, 332, 343, 360, 416, 433, 450, 489, 506, 523, 540, 579, 596, 613, 630, 652, 669, 686, 703, 720, 730, 732, 742, 747, 752, 762, 772

Offset: 1

Author

Paolo P. Lava, Feb 15 2017

Keywords

• nonn
• base
• easy

Comments

All the palindromic numbers in base 9 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 9 is 1030854453981. - Giovanni Resta, Feb 16 2017

Examples

			762 in base 9 is 1036. If we split the number in 103 and 6 we have 3*1 + 0*2 + 1*3 = 6 for the left side and 6*1 = 6 for the right one.
		

Links

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

Crossrefs

Cf. A282107-A282115, A282143-A282149, A282151.

Programs

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,9),i=1..10^3);