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 A282149 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 = 8. 2
 9, 18, 27, 36, 45, 54, 63, 66, 72, 75, 84, 93, 102, 111, 129, 132, 141, 144, 150, 159, 198, 201, 207, 216, 258, 273, 288, 330, 345, 360, 387, 402, 417, 432, 459, 474, 489, 504, 513, 515, 524, 528, 533, 542, 551, 576, 581, 585, 590, 599, 600, 642, 647, 657, 672 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All the palindromic numbers in base 8 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. The first number with this property in all the bases from 2 to 8 is 10296444436. - Giovanni Resta, Feb 16 2017 LINKS Paolo P. Lava, Table of n, a(n) for n = 1..10000 EXAMPLE 672 in base 8 is 1240. If we split the number in 12 and 40 we have 2*1 + 1*2 = 4 for the left side and 4*1 + 0*2 = 4 for the right one. MAPLE with(numtheory): P:=proc(q, h) local a, b, d, j, k, n, s; for n from 1 to q do a:=convert(n, base, h); for k from 1 to trunc(nops(a)/2) do b:=a[k]; a[k]:=a[nops(a)-k+1]; a[nops(a)-k+1]:=b; od; for k from 1 to nops(a)-1 do d:=0; s:=0; for j from 1 to k do if a[j]>0 then s:=s+a[j]*(k-j+1); fi; od; for j from nops(a) by -1 to k+1 do if a[j]>0 then d:=d+a[j]*(j-k); fi; od; if d=s then print(n); break; fi; od; od; end: P(10^3, 8); CROSSREFS Cf. A282107 - A282115, A282143 - A282148, A282150, A282151. Sequence in context: A119310 A037993 A044849 * A114612 A108782 A178734 Adjacent sequences:  A282146 A282147 A282148 * A282150 A282151 A282152 KEYWORD nonn,base,easy AUTHOR Paolo P. Lava, Feb 15 2017 STATUS approved

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Last modified December 11 05:41 EST 2017. Contains 295868 sequences.