A282112 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 = 7.

50, 57, 64, 71, 78, 85, 92, 100, 107, 114, 121, 128, 135, 142, 150, 157, 164, 171, 178, 185, 192, 200, 207, 214, 221, 228, 235, 242, 250, 257, 264, 271, 278, 285, 292, 300, 307, 314, 321, 328, 335, 342, 345, 350, 352, 359, 366, 373, 380, 387, 395, 399, 402, 409

Offset

1,1

Comments

All the palindromic numbers in base 7 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 7 are: 53060873, 55161152, 151009636, 343518281, 505587488, 513015908, ...- Giovanni Resta, Feb 13 2017

Links

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

Example

409 in base 7 is 1123. If j = 2 (digit 2) 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, 7), i=1..10^3);

Crossrefs

Cf. A282107 - A282111, A282113 - A282115.

Sequence in context: A349210 A114504 A227548 * A172468 A046832 A046834

Adjacent sequences: A282109 A282110 A282111 * A282113 A282114 A282115

Keyword

nonn,base,easy

Author

Paolo P. Lava, Feb 06 2017

Status

approved