The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A282114

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A282114

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 = 9.
(history; published version)

#13 by Bruno Berselli at Thu May 30 08:59:23 EDT 2019

STATUS

editing

approved

#12 by Paolo P. Lava at Tue May 28 07:20:58 EDT 2019

MAPLE

P:=proc(n, h) local a, j, k: a:=convert(n, base, h): for k from 1 to nops(a)-1 do

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:

RETURN(n); break: fi: od: end: seq(P(i, 9), i=1..10^3);

#11 by Paolo P. Lava at Tue May 28 07:10:46 EDT 2019

MAPLE

with(numtheory): P:=proc(q, n, h) local a, b, d, j, k, : a:=convert(n, s; base, h): for k from 1 to nops(a)-1 do

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 k-1 do if a[j]>0 then s:=s+a[j]*(k-j); fi; od; for j from nops(a) by -1 to k+1 do

if add(a[j]>0 then d:*(k-j), j=1..k)=d+add(a[j]*(j-k); fi; od; if d, j=s k+1..nops(a)) then printRETURN(n); break; fi; od; od; end: P(10^9, 9);

fi: od: end: seq(P(i, 9), i=1..10^3);

STATUS

approved

editing

#10 by Bruno Berselli at Wed Feb 15 03:29:05 EST 2017

STATUS

proposed

approved

#9 by Paolo P. Lava at Mon Feb 13 09:06:09 EST 2017

STATUS

editing

proposed

#8 by Paolo P. Lava at Mon Feb 13 08:59:32 EST 2017

COMMENTS

Numbers with this property in all the bases from 2 to 9 are:

898958160865, 1518029154732,... - Giovanni Resta, Feb 13 2017

#7 by Paolo P. Lava at Tue Feb 07 05:52:41 EST 2017

COMMENTS

Here the fulcrum is one of the digits while in the sequence from A282143 to A282151 is between two digits.

#6 by Paolo P. Lava at Tue Feb 07 05:44:56 EST 2017

COMMENTS

All the palindromic numbers in base 9 with an odd number of digits belong to the sequence.

#5 by Paolo P. Lava at Tue Feb 07 05:42:45 EST 2017

LINKS

Paolo P. Lava, <a href="/A282114/b282114.txt">Table of n, a(n) for n = 1..10000</a>

#4 by Paolo P. Lava at Tue Feb 07 03:34:02 EST 2017

MAPLE

with(numtheory): P:=proc(q, h) local a, b, c, d, i, j, k, ok, n, s; for n from 1 to q do a:=convert(n, base, h);

for n from 1 to q do a:=convert(n, base, h);