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 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. 18
 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 (list; graph; refs; listen; history; text; internal format)
 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: A198263 A276192 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

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Last modified August 7 19:57 EDT 2020. Contains 336279 sequences. (Running on oeis4.)