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A282111
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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+1..k}{(i-j)*d_i} = Sum_{i=1..j-1}{(j-i)*d_i}. Case x = 6.
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4
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37, 43, 49, 55, 61, 67, 74, 80, 86, 92, 98, 104, 111, 117, 123, 129, 135, 141, 148, 154, 160, 166, 172, 178, 185, 191, 197, 203, 209, 215, 218, 222, 224, 230, 236, 242, 248, 255, 258, 261, 267, 273, 279, 285, 292, 294, 298, 304, 310, 316, 322, 329, 330, 335, 341
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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 6 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.
Numbers with this property in all the bases from 2 to 6 are:
144781, 345440, 743687, 1650704, 4020912, 4270149, 4757093, 6922591, 7102553, 7406643, 7677171, 7823009, 8853188, 12444016, 14457746, 14853520, 14861718, 15794512, 15994195, 17375742, 20450682, 20802565, 22173561, 22186557, 25268754, 261656297, 26648201, 27740672, ...
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LINKS
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EXAMPLE
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304 in base 6 is 1224. If j = 2 (the first 2 from right) we have 2*1 + 1*2 = 4 for the left side and 4*1 = 4 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, 6), 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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