A282146 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 = 5.

6, 12, 18, 24, 27, 30, 33, 39, 51, 54, 60, 81, 90, 102, 111, 120, 126, 128, 134, 135, 150, 156, 165, 177, 186, 195, 207, 216, 228, 237, 246, 252, 255, 261, 270, 282, 291, 300, 303, 312, 321, 333, 342, 354, 363, 372, 376, 378, 387, 396, 405, 408, 417, 429, 438, 447

Offset

1,1

Comments

All the palindromic numbers in base 5 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 5 are: 3120, 9615, 10366, 16610, 17812, 22129, 33329, 100726, 163800, 202039, 208172, 212636, 258221, 270337, 298575, 420240, 462608, 475782, 492420, 523679, 549537, 550200, 587842, 594511, 610273, 655350, 671844, 675872, 681280, 730161, 738480, 840798, 842614, 848655, 855973, 925515, 987751, ...

Links

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

Example

447 in base 5 is 3242. If we split the number in 32 and 42 we have 2*1 + 3*2 = 8 for the left side and 4*1 + 2*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, 5), i=1..10^3);

Crossrefs

Cf. A282107 - A282115, A282143 - A282145, A282147 - A282151.

Sequence in context: A044846 A037917 A336339 * A204879 A326696 A097603

Adjacent sequences: A282143 A282144 A282145 * A282147 A282148 A282149

Keyword

nonn,base,easy

Author

Paolo P. Lava, Giovanni Resta, Feb 07 2017

Status

approved