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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. 4
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
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
Sequence in context: A155849 A295154 A224319 * A110563 A178777 A139773
KEYWORD
nonn,base,easy
AUTHOR
Paolo P. Lava, Feb 06 2017
STATUS
approved

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Last modified June 23 22:09 EDT 2024. Contains 373661 sequences. (Running on oeis4.)