A282109 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 = 4.

17, 21, 25, 29, 34, 38, 42, 46, 51, 55, 59, 63, 66, 68, 70, 74, 78, 83, 84, 87, 91, 95, 100, 116, 129, 136, 145, 152, 161, 168, 177, 184, 197, 204, 213, 220, 229, 236, 245, 252, 257, 259, 263, 264, 267, 271, 272, 273, 280, 289, 296, 305, 312, 325, 332, 336, 341

Offset

1,1

Comments

All the palindromic numbers in base 4 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.

Links

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

Example

83 in base 4 is 1103. If j = 2 (digit 0) we have 1*1 + 1*2 = 3 for the left side and 3*1 = 3 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, 4), i=1..10^3);

Crossrefs

A282107, A282108, A282110 - A282115.

Sequence in context: A039502 A039505 A166875 * A373583 A307863 A128546

Adjacent sequences: A282106 A282107 A282108 * A282110 A282111 A282112

Keyword

base,nonn,easy

Author

Paolo P. Lava, Feb 06 2017

Status

approved