A282148 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 = 7.

8, 16, 24, 32, 40, 48, 51, 56, 59, 67, 75, 83, 99, 102, 110, 112, 118, 153, 155, 168, 198, 211, 224, 254, 267, 280, 297, 310, 323, 336, 344, 346, 354, 357, 362, 370, 392, 397, 400, 405, 413, 443, 456, 469, 499, 512, 525, 542, 555, 568, 581, 598, 611, 624, 641, 654

Offset

1,1

Comments

All the palindromic numbers in base 7 with an even number of digits belong to the sequence.

Here the fulcrum is between two digits while in the sequence from A282107 to A282115 is one of the digits.

The first number with this property in all the bases from 2 to 7 is

86964945. - Giovanni Resta, Feb 15 2017

Links

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

Example

641 in base 7 is 1604. If we split the number in 16 and 04 we have 6*1 + 1*2 = 8 for the left side and 0*1 + 4*2 = 8 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+1), j=1..k)=add(a[j]*(j-k), j=k+1..nops(a))
then RETURN(n); break: fi: od: end: seq(P(i, 7), i=1..10^3);

Crossrefs

Cf. A282107 - A282115, A282143 - A282147.

Sequence in context: A144566 A037989 A044848 * A277780 A044893 A185359

Adjacent sequences: A282145 A282146 A282147 * A282149 A282150 A282151

Keyword

nonn,base,easy

Author

Paolo P. Lava, Feb 15 2017

Status

approved