A369603 S is a "boomerang sequence": adding 9 to each digit of S and following the result with a comma leaves S unchanged.

10, 9, 18, 10, 17, 10, 9, 10, 16, 10, 9, 18, 10, 9, 10, 15, 10, 9, 18, 10, 17, 10, 9, 18, 10, 9, 10, 14, 10, 9, 18, 10, 17, 10, 9, 10, 16, 10, 9, 18, 10, 17, 10, 9, 18, 10, 9, 10, 13, 10, 9, 18, 10, 17, 10, 9, 10, 16, 10, 9, 18, 10, 9, 10, 15, 10, 9, 18, 10, 17, 10, 9, 10, 16, 10, 9, 18, 10, 17, 10, 9, 18, 10, 9

Offset: 1

Author

Eric Angelini and Giorgos Kalogeropoulos, Jan 27 2024

Keywords

• base
• nonn

Comments

Lexicographically earliest sequence starting with a(1) = 10.

The only integers that appear in the sequence are 9, 10, 11, 12, 13, 14, 15, 16, 17 and 18.

Is this (apart from the first term) the same as A103700? - R. J. Mathar, Feb 12 2024

Examples

			Adding 9 to 1 (the 1st digit of 10) gives 10
Adding 9 to 0 (the 2nd digit of 10) gives 9
Adding 9 to 9 (the only digit of 9) gives 18
Adding 9 to 1 (the 1st digit of 18) gives 10
Adding 9 to 8 (the 2nd digit of 18) gives 17, etc.
We see that the last column above is the sequence S itself.
		

Links

• Éric Angelini and Giorgos Kalogeropoulos, The same sequence but differently, personal blog, Jan 24th 2024.

Crossrefs

Cf. A103700, A369604, A369798, A369823, A369824.

Programs

Mathematica

a[1]=10;a[n_]:=a[n]=Flatten[IntegerDigits/@Array[a,n-1]][[n]]+9;Array[a,100]

Python

from itertools import islice
def agen(): # generator of terms
    an, digits = 10, [0]
    while True:
        yield an
        an = 9 + digits.pop(0)
        digits += list(map(int, str(an)))
print(list(islice(agen(), 84))) # Michael S. Branicky, Jan 27 2024