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 A282110 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 = 5. 3
 26, 31, 36, 41, 46, 52, 57, 62, 67, 72, 78, 83, 88, 93, 98, 104, 109, 114, 119, 124, 127, 130, 132, 137, 142, 147, 153, 155, 158, 163, 168, 173, 179, 180, 184, 189, 194, 199, 205, 230, 251, 254, 259, 260, 264, 269, 274, 276, 285, 301, 310, 326, 335, 351, 360, 381 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All the palindromic numbers in base 5 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 5 are: 78, 650, 1550, 4368, 4433, 4805, 6913, 7410, 16709, 31824, 35175, 41216, 104272, 107584, 132285, 144781, 165059, 173305, 174096, 190468, 195473, 201900, 205005, 205261, 214432, 231521, 243984, 275026, 278528, 295275, 304562, 313769, ... LINKS Paolo P. Lava, Table of n, a(n) for n = 1..10000 EXAMPLE 137 in base 5 is 1022. If j=2 (the second 2 from right) we have 0*1 + 1*2 = 2 for the left side and 2*1 = 2 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, 5), i=1..10^3); CROSSREFS CF. A282107 - A282109, A282111 - A282115. Sequence in context: A178098 A278779 A045163 * A275192 A046292 A259041 Adjacent sequences:  A282107 A282108 A282109 * A282111 A282112 A282113 KEYWORD base,nonn,easy AUTHOR Paolo P. Lava, Feb 06 2017 STATUS approved

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Last modified September 17 01:53 EDT 2021. Contains 347478 sequences. (Running on oeis4.)