A369604 T is a "boomerang sequence": adding 9 to the 1st digit of T, 10 to the 2nd digit of T, 11 to the 3rd digit of T, 12 to the 4th digit of T, 13 to the 5th digit of T, 14 to the 6th digit of T, etc., and following each result with a comma leaves T unchanged.

10, 10, 12, 12, 14, 16, 16, 18, 18, 22, 20, 26, 22, 28, 24, 32, 26, 34, 29, 30, 31, 30, 33, 38, 35, 36, 37, 44, 39, 42, 42, 42, 43, 48, 46, 48, 47, 55, 50, 48, 52, 51, 54, 52, 56, 57, 58, 64, 60, 63, 62, 66, 64, 69, 67, 68, 68, 75, 71, 70, 73, 72, 75, 74, 77, 77, 79, 84, 81, 84, 83, 88, 85, 89, 88, 89, 90, 86, 91

Offset: 1

Author

Eric Angelini and Giorgos Kalogeropoulos, Jan 27 2024

Keywords

• base
• nonn

Comments

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

Examples

			Adding  9 to 1 (the 1st digit of 10) gives 10
Adding 10 to 0 (the 2nd digit of 10) gives 10
Adding 11 to 1 (the 1st digit of 10) gives 12
Adding 12 to 0 (the 2nd digit of 10) gives 12
Adding 13 to 1 (the 1st digit of 12) gives 14
Adding 14 to 2 (the 2nd digit of 12) gives 16, etc.
We see that the last column above is the sequence T itself.
		

Links

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

Crossrefs

Cf. A103700, A369603, A369798, A369823, A369824.

Programs

Mathematica

a[1]=10;a[n_]:=a[n]=Flatten[IntegerDigits/@Array[a,n-1]][[n]]+8+n;Array[a,100]

Python

from itertools import count, islice
def agen(): # generator of terms
    an, digits = 10, [0]
    for n in count(2):
        yield an
        an = n + 8 + digits.pop(0)
        digits += list(map(int, str(an)))
print(list(islice(agen(), 79))) # Michael S. Branicky, Jan 27 2024