A282147 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 = 6.

7, 14, 21, 28, 35, 38, 42, 45, 52, 59, 73, 76, 83, 84, 115, 126, 146, 157, 168, 188, 199, 210, 217, 219, 226, 228, 233, 252, 257, 259, 270, 290, 301, 312, 332, 343, 354, 363, 374, 385, 405, 416, 427, 434, 438, 445, 456, 476, 487, 498, 504, 507, 518, 529, 549, 560

Offset: 1

Author

Paolo P. Lava, Giovanni Resta, Feb 07 2017

Keywords

• nonn
• base
• easy

Comments

All the palindromic numbers in base 6 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.

Numbers with this property in all the bases from 2 to 6 are:

420240, 610273, 848655, 855973, 987751, 1830038, 2347657, 3480366, 3519545, 4832865, 5141958, 6050107, 9010530, 9770426, 11520023, 13951022, 14036167, 14694080, 15106072, 16487203, 24125707, 25209012, ...

Examples

			580 in base 6 is 2404. If we split the number in 24 and 04 we have 4*1 + 2*2 = 8 for the left side and 0*1 + 4*2 = 8 for the right one.
		

Links

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

Crossrefs

Cf. A282107 - A282115, A282143 - A282146, A282148 - A282151.

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+1),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);