A083678 -id:A083678 - cp's OEIS frontend

A093472 (2n+1)-digit anti-palindromic numbers or numberdromes, whose first and last digits add to ten, second and next-to-last add to ten and so on with the central digit a 5.

159, 258, 357, 456, 555, 654, 753, 852, 951, 11599, 12589, 13579, 14569, 15559, 16549, 17539, 18529, 19519, 21598, 22588, 23578, 24568, 25558, 26548, 27538, 28528, 29518, 31597, 32587, 33577, 34567, 35557, 36547, 37537, 38527, 39517

Offset: 0

Michael Joseph Halm, May 13 2004

			a(1) = 159 because at least three digits are required, so that n = 1, m = 1 yields a(1) = 100+50+(10-1) = 159

Cf. A083678.

a(n) = (10^(m+1))n+5(10^m)+(10^m-n)

A299539 Numbers n = d_1 d_2 ... d_k (in base 10) such that d_i + d_{k+1-i} = 10 for i = 1..k.

Original entry on oeis.org

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

Offset: 1

Rémy Sigrist, Mar 05 2018

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

			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.

Robert E. Kennedy and Curtis N. Cooper, Bach, 5465, and Upside-Down Numbers, The College Mathematics Journal, Vol. 18, No. 2 (Mar., 1987), pp. 111-115.
Giovanni Resta, Upside-down numbers, Numbers Aplenty.

Cf. A052382, A083678, A093472, A284811.

Cf. also A060109 (Morse code of numbers).

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:
Res; # Robert Israel, Mar 06 2018

Select[Range[4300], AllTrue[#1[[1 ;; #2]] + Reverse@ #1[[-#2 ;; -1]], # == 10 &] & @@ {#, Ceiling[Length[#]/2]} &@ IntegerDigits[#] &] (* Michael De Vlieger, Nov 04 2020 *)

is(n) = my (d=digits(n)); Set(d+Vecrev(d))==Set(10)

cp's OEIS Frontend

A093472 (2n+1)-digit anti-palindromic numbers or numberdromes, whose first and last digits add to ten, second and next-to-last add to ten and so on with the central digit a 5.

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A299539 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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