A282107 Numbers n with k digits in base x (MSD(n)_x=d_k, LSD(n)_x=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 = 2.

5, 7, 10, 14, 17, 20, 21, 27, 28, 31, 34, 35, 39, 40, 42, 49, 54, 56, 57, 62, 65, 68, 70, 73, 78, 80, 84, 85, 93, 98, 99, 107, 108, 112, 114, 119, 124, 127, 130, 133, 136, 140, 141, 146, 147, 155, 156, 160, 161, 167, 168, 170, 175, 177, 186, 196, 198, 201, 214

Offset

1,1

Comments

All the palindromic numbers in base 2 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

897 in base 2 is 1110000001. If j = 7 (the first 0 from left) we have 1*1 + 1*2 + 1*3 = 6 for the left side and 0*1 + 0*2 + 0*3 + 0*4 + 0*5 + 1*6 = 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), 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. A282108 - A282115.

Sequence in context: A297000 A356218 A354939 * A022441 A156243 A020942

Adjacent sequences: A282104 A282105 A282106 * A282108 A282109 A282110

Keyword

nonn,base,easy

Author

Paolo P. Lava, Feb 06 2017

Status

approved