The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A282151 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A282151

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 = 10.
(history; published version)

#13 by Bruno Berselli at Thu May 30 09:00:28 EDT 2019

STATUS

editing

approved

#12 by Paolo P. Lava at Tue May 28 06:57:41 EDT 2019

MAPLE

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

#11 by Paolo P. Lava at Tue May 28 05:58:26 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+1), j=1..k)=add(a[j]*(j-k), j=k+1..nops(a)) then n; fi: od: end:

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

#10 by Paolo P. Lava at Tue May 28 05:57:40 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 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 add(a[j]>0 then d:=d*(k-j+1), j=1..k)=add(a[j]*(j-k); fi; od; if d, j=s k+1..nops(a)) then print(n); break; fi; od; : od; : end: P(10^3, 10);

seq(P(i, 10), i=1..10^3);

STATUS

approved

editing

#9 by Bruno Berselli at Mon Sep 24 08:13:45 EDT 2018

STATUS

proposed

approved

#8 by Paolo P. Lava at Mon Sep 24 08:11:41 EDT 2018

STATUS

editing

proposed

#7 by Paolo P. Lava at Mon Sep 24 08:11:38 EDT 2018

NAME

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 = 610.

COMMENTS

All the palindromic numbers in base 6 10 with an even number of digits belong to the sequence.

STATUS

proposed

editing

#6 by Paolo P. Lava at Mon Sep 24 08:07:45 EDT 2018

STATUS

editing

proposed

#5 by Paolo P. Lava at Mon Sep 24 08:07:42 EDT 2018

COMMENTS

All the palindromic numbers in base 10 6 with an even number of digits belong to the sequence.

STATUS

approved

editing

#4 by Bruno Berselli at Fri Feb 17 08:31:19 EST 2017

STATUS

proposed

approved