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A299539
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Numbers n = d_1 d_2 ... d_k (in base 10) such that d_i + d_{k+1-i} = 10 for i = 1..k.
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1
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5, 19, 28, 37, 46, 55, 64, 73, 82, 91, 159, 258, 357, 456, 555, 654, 753, 852, 951, 1199, 1289, 1379, 1469, 1559, 1649, 1739, 1829, 1919, 2198, 2288, 2378, 2468, 2558, 2648, 2738, 2828, 2918, 3197, 3287, 3377, 3467, 3557, 3647, 3737, 3827, 3917, 4196, 4286
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refs;
listen;
history;
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internal format)
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OFFSET
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1,1
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COMMENTS
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These numbers are also called upside-down numbers.
All terms belong to A052382 (zeroless numbers).
The central digit of the terms with an odd number of digits is always 5.
This sequence can be partitioned into three sets: { 5 }, A083678 and A093472.
This sequence has similarities with A284811: here d_i + d_{k+1-i} = 10, there d_i + d_{k+1-i} = 9.
These numbers have a palindromic Morse code representation (see A060109). To get all numbers with this property one has to include 0 and terms with corresponding "interior" digits 5 replaced by digits 0, e.g., 5 -> 0, 159 -> 109, 555 -> 505, 1559 -> 1009, 15559 -> {10009, 10509, 15059}. - M. F. Hasler, Nov 02 2020
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LINKS
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EXAMPLE
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1 + 9 = 10 and 5 + 5 = 10 and 9 + 1 = 10, hence 159 belongs to this sequence.
4 + 2 = 6, hence 42 does not belong to this sequence.
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MAPLE
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Res:= NULL;
for d from 1 to 3 do
for x from 0 to 9^(d-1)-1 do
L:= convert(9^(d-1)+x, base, 9)[1..d-1];
Res:= Res, 5*10^(d-1)+add((1+L[-i])*10^(2*d-1-i)+(9-L[-i])*10^(i-1), i=1..d-1)
od;
for x from 0 to 9^d-1 do
L:= convert(9^d+x, base, 9)[1..d];
Res:= Res, add((1+L[-i])*10^(2*d-i)+(9-L[-i])*10^(i-1), i=1..d)
od
od:
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MATHEMATICA
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Select[Range[4300], AllTrue[#1[[1 ;; #2]] + Reverse@ #1[[-#2 ;; -1]], # == 10 &] & @@ {#, Ceiling[Length[#]/2]} &@ IntegerDigits[#] &] (* Michael De Vlieger, Nov 04 2020 *)
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PROG
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(PARI) is(n) = my (d=digits(n)); Set(d+Vecrev(d))==Set(10)
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CROSSREFS
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Cf. also A060109 (Morse code of numbers).
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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