A282114 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 = 9.

82, 91, 100, 109, 118, 127, 136, 145, 154, 164, 173, 182, 191, 200, 209, 218, 227, 236, 246, 255, 264, 273, 282, 291, 300, 309, 318, 328, 337, 346, 355, 364, 373, 382, 391, 400, 410, 419, 428, 437, 446, 455, 464, 473, 482, 492, 501, 510, 519, 528, 537, 546, 555

Offset

1,1

Comments

All the palindromic numbers in base 9 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 9 are:

898958160865, 1518029154732,... - Giovanni Resta, Feb 13 2017

Links

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

Example

3485 in base 9 is 4702. If j = 3 (digit 7) we have 4*1 = 4 for tyhe left side and 0*1 + 2*2 = 4 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, 9), i=1..10^3);

Crossrefs

Cf. A282107 - A282113, A282115.

Sequence in context: A303885 A305278 A025370 * A099067 A304891 A316573

Adjacent sequences: A282111 A282112 A282113 * A282115 A282116 A282117

Keyword

nonn,base,easy

Author

Paolo P. Lava, Feb 06 2017

Status

approved