

A282113


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}{(ij)*d_i} = Sum_{i=1..j1}{(ji)*d_i}. Case x = 8.


3



65, 73, 81, 89, 97, 105, 113, 121, 130, 138, 146, 154, 162, 170, 178, 186, 195, 203, 211, 219, 227, 235, 243, 251, 260, 268, 276, 284, 292, 300, 308, 316, 325, 333, 341, 349, 357, 365, 373, 381, 390, 398, 406, 414, 422, 430, 438, 446, 455, 463, 471, 479, 487, 495
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OFFSET

1,1


COMMENTS

All the palindromic numbers in base 8 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 8 are: 2438269535, 6936679443, 8657968788, 11107027008, 21733512704, ...  Giovanni Resta, Feb 13 2017


LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..10000


EXAMPLE

1084 in base 8 is 2074. If j = 2 (digit 7) we have 0*1 + 2*2 = 4 for the left side and 4*1 = 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 2 to nops(a)1 do d:=0; s:=0;
for j from 1 to k1 do if a[j]>0 then s:=s+a[j]*(kj); fi; od; for j from nops(a) by 1 to k+1 do
if a[j]>0 then d:=d+a[j]*(jk); fi; od; if d=s then print(n); break; fi; od; od; end: P(10^9, 8);


CROSSREFS

Cf. A282107  A282112, A282114, A282115.
Sequence in context: A173379 A095535 A095523 * A060877 A113688 A214484
Adjacent sequences: A282110 A282111 A282112 * A282114 A282115 A282116


KEYWORD

nonn,base,easy


AUTHOR

Paolo P. Lava, Feb 06 2017


STATUS

approved



