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A282107
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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.
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18
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MAPLE
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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);
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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