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%I #26 Feb 04 2021 17:33:00
%S 0,5,19,28,37,46,55,64,73,82,91,109,159,208,258,307,357,406,456,505,
%T 555,604,654,703,753,802,852,901,951,1009,1199,1289,1379,1469,1559,
%U 1649,1739,1829,1919,2008,2198,2288,2378,2468,2558,2648,2738,2828,2918,3007
%N Numbers with palindromic Morse code A060109.
%C Also, numbers whose decimal digits (d[0], ..., d[n]) are such that for all k = 0..n, d[k] + d[n-k] = 0 (mod 10). In particular, if the number of digits n+1 is odd, the middle digit must be either 5 or 0.
%C The variant A299539 is obtained by excluding terms with a digit 0, i.e., removing all terms that are in A011540, or taking intersection with zeroless numbers A052382. - _M. F. Hasler_, Nov 25 2020
%F Sequence is { N | A060109(N) is in A002113 }.
%e The Morse code for digits is "-----" for 0, ".----" for 1, "..---" for 2, ..., "....." for 5, "-...." for 6, ..., "----." for 9. (In A060109 a dot is coded with a digit 1 and a dash with a digit 2.)
%e We see that 0 and 5 are the only digits with palindromic Morse code, this yields a(1) and a(2).
%e Two digit numbers must be of the form 10*a + (10-a), with a = 1, ..., 9, in order to have palindromic Morse code. This yields the 9 terms a(3), ..., a(11).
%e Three-digit terms must have 0 or 5 as middle digit and yield a two-digit term when that middle digit is deleted: this yields the next 18 terms a(12 .. 29).
%t With[{a = Association@ Array[# -> If[# < 6, PadRight[ConstantArray[1, #], 5, 2], PadRight[ConstantArray[2, # - 5], 5, 1]] &, 10, 0]}, Select[Range[0, 3007], PalindromeQ[Flatten@ Riffle[Map[Lookup[a, #] &, IntegerDigits[#]], 0]] &]] (* _Michael De Vlieger_, Nov 02 2020 *)
%o (PARI) select( is(n)=(Vecrev(n=digits(n))+n)%10==0, [0..3333])
%Y Cf. A060109 (Morse code of n), A002113 (palindromes), A004086 (reverse n), A299539 (variant without the terms with digit 0).
%K nonn,base
%O 1,2
%A _M. F. Hasler_, Nov 02 2020
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