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A282145
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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 = 4.
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3
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5, 10, 15, 18, 20, 23, 33, 40, 53, 60, 65, 67, 72, 80, 85, 92, 98, 105, 118, 125, 130, 132, 137, 150, 157, 160, 163, 170, 183, 190, 193, 195, 202, 212, 215, 222, 235, 240, 255, 260, 261, 268, 274, 281, 288, 294, 301, 307, 314, 320, 321, 326, 333, 339, 340, 346
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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 4 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.
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LINKS
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EXAMPLE
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222 in base 4 is 3132. If we split the number in 31 and 32 we have 1*1 + 3*2 = 7 for the left side and 3*1 + 2*2 = 7 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+1), j=1..k)=add(a[j]*(j-k), j=k+1..nops(a))
then RETURN(n); break: fi: od: end: seq(P(i, 4), 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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