%I #12 May 30 2019 08:59:05

%S 37,43,49,55,61,67,74,80,86,92,98,104,111,117,123,129,135,141,148,154,

%T 160,166,172,178,185,191,197,203,209,215,218,222,224,230,236,242,248,

%U 255,258,261,267,273,279,285,292,294,298,304,310,316,322,329,330,335,341

%N 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 = 6.

%C All the palindromic numbers in base 6 with an odd number of digits belong to the sequence.

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

%C Numbers with this property in all the bases from 2 to 6 are:

%C 144781, 345440, 743687, 1650704, 4020912, 4270149, 4757093, 6922591, 7102553, 7406643, 7677171, 7823009, 8853188, 12444016, 14457746, 14853520, 14861718, 15794512, 15994195, 17375742, 20450682, 20802565, 22173561, 22186557, 25268754, 261656297, 26648201, 27740672, ...

%H Paolo P. Lava, <a href="/A282111/b282111.txt">Table of n, a(n) for n = 1..10000</a>

%e 304 in base 6 is 1224. If j = 2 (the first 2 from right) we have 2*1 + 1*2 = 4 for the left side and 4*1 = 4 for the right one.

%p P:=proc(n,h) local a,j,k: a:=convert(n, base, h):

%p for k from 1 to nops(a)-1 do

%p if add(a[j]*(k-j),j=1..k)=add(a[j]*(j-k),j=k+1..nops(a)) then

%p RETURN(n); break: fi: od: end: seq(P(i,6),i=1..10^3);

%Y Cf. A282107 - A282110, A282112 - A282115.

%K nonn,base,easy

%O 1,1

%A _Paolo P. Lava_, Feb 06 2017