A282143 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 = 2.

3, 6, 9, 12, 15, 18, 19, 24, 25, 30, 33, 36, 38, 45, 48, 50, 51, 60, 63, 66, 69, 72, 75, 76, 81, 87, 90, 96, 100, 102, 105, 117, 120, 126, 129, 131, 132, 138, 143, 144, 150, 152, 153, 162, 165, 174, 179, 180, 189, 192, 193, 195, 200, 204, 205, 210, 219, 231, 234

Offset

1,1

Comments

All the palindromic numbers in base 2 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

143 in base 2 is 10001111. If we split the number in 10001 and 111 we have 1*1 + 0*2 + 0*3 + 0*4 + 1*5 = 6 for the left side and 1*1 + 1*2 + 1*3 = 6 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, 2), i=1..10^3);

Crossrefs

Cf. A282107 - A282115, A282144 - A282151.

Sequence in context: A276192 A347404 A329771 * A214813 A119888 A305495

Adjacent sequences: A282140 A282141 A282142 * A282144 A282145 A282146

Keyword

nonn,base,easy

Author

Paolo P. Lava, Giovanni Resta, Feb 07 2017

Status

approved