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A332155 Numbers with palindromic Morse code A060109. 0
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 (list; graph; refs; listen; history; text; internal format)
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 * A061388 A299539 A270865

Adjacent sequences:  A332152 A332153 A332154 * A332156 A332157 A332158

KEYWORD

nonn,base

AUTHOR

M. F. Hasler, Nov 02 2020

STATUS

approved

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Last modified June 19 18:02 EDT 2021. Contains 345144 sequences. (Running on oeis4.)