A332155 Numbers with palindromic Morse code A060109.

0, 5, 19, 28, 37, 46, 55, 64, 73, 82, 91, 109, 159, 208, 258, 307, 357, 406, 456, 505, 555, 604, 654, 703, 753, 802, 852, 901, 951, 1009, 1199, 1289, 1379, 1469, 1559, 1649, 1739, 1829, 1919, 2008, 2198, 2288, 2378, 2468, 2558, 2648, 2738, 2828, 2918, 3007

Offset

1,2

Comments

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.

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

Links

Table of n, a(n) for n=1..50.

Formula

Sequence is { N | A060109(N) is in A002113 }.

Example

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.)
We see that 0 and 5 are the only digits with palindromic Morse code, this yields a(1) and a(2).
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).
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).

Mathematica

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 *)

Prog

(PARI) select( is(n)=(Vecrev(n=digits(n))+n)%10==0, [0..3333])

Crossrefs

Cf. A060109 (Morse code of n), A002113 (palindromes), A004086 (reverse n), A299539 (variant without the terms with digit 0).

Sequence in context: A119238 A218885 A198791 * A366211 A061388 A299539

Adjacent sequences: A332152 A332153 A332154 * A332156 A332157 A332158

Keyword

nonn,base

Author

M. F. Hasler, Nov 02 2020

Status

approved