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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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..48.

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

EXAMPLE

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.

MAPLE

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

PROG

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

CROSSREFS

Cf. A052382, A083678, A093472, A284811.

Sequence in context: A218885 A198791 A061388 * A270865 A106072 A106062

Adjacent sequences:  A299536 A299537 A299538 * A299540 A299541 A299542

KEYWORD

nonn,base,easy

AUTHOR

Rémy Sigrist, Mar 05 2018

STATUS

approved

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Last modified October 29 21:18 EDT 2020. Contains 338074 sequences. (Running on oeis4.)