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A282110 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 = 5. 4
26, 31, 36, 41, 46, 52, 57, 62, 67, 72, 78, 83, 88, 93, 98, 104, 109, 114, 119, 124, 127, 130, 132, 137, 142, 147, 153, 155, 158, 163, 168, 173, 179, 180, 184, 189, 194, 199, 205, 230, 251, 254, 259, 260, 264, 269, 274, 276, 285, 301, 310, 326, 335, 351, 360, 381 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All the palindromic numbers in base 5 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 5 are: 78, 650, 1550, 4368, 4433, 4805, 6913, 7410, 16709, 31824, 35175, 41216, 104272, 107584, 132285, 144781, 165059, 173305, 174096, 190468, 195473, 201900, 205005, 205261, 214432, 231521, 243984, 275026, 278528, 295275, 304562, 313769, ...
LINKS
EXAMPLE
137 in base 5 is 1022. If j=2 (the second 2 from right) we have 0*1 + 1*2 = 2 for the left side and 2*1 = 2 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, 5), i=1..10^3);
CROSSREFS
Sequence in context: A178098 A278779 A045163 * A275192 A046292 A259041
KEYWORD
base,nonn,easy
AUTHOR
Paolo P. Lava, Feb 06 2017
STATUS
approved

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Last modified March 28 12:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)