A282145 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 = 4.

5, 10, 15, 18, 20, 23, 33, 40, 53, 60, 65, 67, 72, 80, 85, 92, 98, 105, 118, 125, 130, 132, 137, 150, 157, 160, 163, 170, 183, 190, 193, 195, 202, 212, 215, 222, 235, 240, 255, 260, 261, 268, 274, 281, 288, 294, 301, 307, 314, 320, 321, 326, 333, 339, 340, 346

Offset

1,1

Comments

All the palindromic numbers in base 4 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

222 in base 4 is 3132. If we split the number in 31 and 32 we have 1*1 + 3*2 = 7 for the left side and 3*1 + 2*2 = 7 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, 4), i=1..10^3);

Crossrefs

Cf. A282107 - A282115, A282143, A282144, A282146 - A282151.

Sequence in context: A313673 A313674 A337789 * A313675 A313676 A344958

Adjacent sequences: A282142 A282143 A282144 * A282146 A282147 A282148

Keyword

nonn,base,easy

Author

Paolo P. Lava, Giovanni Resta, Feb 07 2017

Status

approved