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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. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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, ...

LINKS

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

EXAMPLE

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.

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);

CROSSREFS

Cf. A282107 - A282110, A282112 - A282115.

Sequence in context: A155849 A295154 A224319 * A110563 A178777 A139773

Adjacent sequences:  A282108 A282109 A282110 * A282112 A282113 A282114

KEYWORD

nonn,base,easy

AUTHOR

Paolo P. Lava, Feb 06 2017

STATUS

approved

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Last modified August 12 23:19 EDT 2020. Contains 336440 sequences. (Running on oeis4.)