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

1,1

Comments

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

Links

Table of n, a(n) for n=1..79.

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A380997 A377565 A111381 * A063660 A354049 A354113

Adjacent sequences: A369601 A369602 A369603 * A369605 A369606 A369607

Keyword

base,nonn

Author

Eric Angelini and Giorgos Kalogeropoulos, Jan 27 2024

Status

approved