A282108 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+1..k}{(i-j)*d_i} = Sum_{i=1..j-1}{(j-i)*d_i}. Case x = 3.

10, 13, 16, 20, 23, 26, 29, 30, 32, 35, 39, 48, 55, 60, 64, 69, 73, 78, 82, 87, 90, 91, 96, 100, 105, 112, 117, 121, 130, 137, 142, 144, 146, 151, 155, 160, 164, 165, 169, 173, 178, 180, 182, 187, 192, 194, 203, 207, 212, 219, 224, 233, 234, 242, 246, 247, 256

Offset

1,1

Comments

All the palindromic numbers in base 3 with an odd number of digits belong to the sequence.

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

Links

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

Example

35 in base 3 is 1022. If j = 2 (second 2 from the right) we have 0*1 + 1*2 = 2 for the left side and 2*1 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), j=1..k)=add(a[j]*(j-k), j=k+1..nops(a))
then RETURN(n); break: fi: od: end: seq(P(i, 3), i=1..10^3);

Crossrefs

Cf. A282107, A282109 - A282115.

Sequence in context: A345508 A153045 A055984 * A306035 A339077 A373278

Adjacent sequences: A282105 A282106 A282107 * A282109 A282110 A282111

Keyword

base,nonn,easy

Author

Paolo P. Lava, Feb 06 2017

Status

approved