A282111 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 = 6.

37, 43, 49, 55, 61, 67, 74, 80, 86, 92, 98, 104, 111, 117, 123, 129, 135, 141, 148, 154, 160, 166, 172, 178, 185, 191, 197, 203, 209, 215, 218, 222, 224, 230, 236, 242, 248, 255, 258, 261, 267, 273, 279, 285, 292, 294, 298, 304, 310, 316, 322, 329, 330, 335, 341

Offset: 1

Author

Paolo P. Lava, Feb 06 2017

Keywords

• nonn
• base
• easy

Comments

All the palindromic numbers in base 6 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 6 are:

144781, 345440, 743687, 1650704, 4020912, 4270149, 4757093, 6922591, 7102553, 7406643, 7677171, 7823009, 8853188, 12444016, 14457746, 14853520, 14861718, 15794512, 15994195, 17375742, 20450682, 20802565, 22173561, 22186557, 25268754, 261656297, 26648201, 27740672, ...

Examples

			304 in base 6 is 1224. If j = 2 (the first 2 from right) we have 2*1 + 1*2 = 4 for the left side and 4*1 = 4 for the right one.
		

Links

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

Crossrefs

Cf. A282107 - A282110, A282112 - A282115.

Programs

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,6),i=1..10^3);