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A282110 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 = 5. 3

%I

%S 26,31,36,41,46,52,57,62,67,72,78,83,88,93,98,104,109,114,119,124,127,

%T 130,132,137,142,147,153,155,158,163,168,173,179,180,184,189,194,199,

%U 205,230,251,254,259,260,264,269,274,276,285,301,310,326,335,351,360,381

%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 = 5.

%C All the palindromic numbers in base 5 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 5 are: 78, 650, 1550, 4368, 4433, 4805, 6913, 7410, 16709, 31824, 35175, 41216, 104272, 107584, 132285, 144781, 165059, 173305, 174096, 190468, 195473, 201900, 205005, 205261, 214432, 231521, 243984, 275026, 278528, 295275, 304562, 313769, ...

%H Paolo P. Lava, <a href="/A282110/b282110.txt">Table of n, a(n) for n = 1..10000</a>

%e 137 in base 5 is 1022. If j=2 (the second 2 from right) we have 0*1 + 1*2 = 2 for the left side and 2*1 = 2 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,5),i=1..10^3);

%Y CF. A282107 - A282109, A282111 - A282115.

%K base,nonn,easy

%O 1,1

%A _Paolo P. Lava_, Feb 06 2017

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Last modified September 28 07:46 EDT 2020. Contains 337394 sequences. (Running on oeis4.)