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 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. 18
 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 (list; graph; refs; listen; history; text; internal format)
 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: A065503 A152001 A297000 * A022441 A156243 A020942 Adjacent sequences:  A282104 A282105 A282106 * A282108 A282109 A282110 KEYWORD nonn,base,easy AUTHOR Paolo P. Lava, Feb 06 2017 STATUS approved

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Last modified August 12 23:19 EDT 2020. Contains 336440 sequences. (Running on oeis4.)