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 A282115 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 = 10. 18
 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 404, 414, 424, 434, 444, 454, 464, 474, 484, 494, 505, 515, 525, 535, 545, 555, 565, 575, 585, 595, 606, 616, 626 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All the palindromic numbers in base 10 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 10467: if j = 2 (digit 6) we have 4*1 + 0*2 + 1*3 = 7 for the left side and 7*1 = 7 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, 10), i=1..10^3); CROSSREFS Cf. A282107 - A282114. Sequence in context: A303571 A303573 A050661 * A116642 A283590 A279173 Adjacent sequences:  A282112 A282113 A282114 * A282116 A282117 A282118 KEYWORD nonn,base,easy AUTHOR Paolo P. Lava, Feb 06 2017 STATUS approved

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Last modified September 21 15:47 EDT 2021. Contains 347598 sequences. (Running on oeis4.)