A369603 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

LINKS

Table of n, a(n) for n=1..84.

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 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.

MATHEMATICA

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

PROG

(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

CROSSREFS

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

Sequence in context: A063596 A360382 A284518 * A309660 A341821 A184959

Adjacent sequences: A369600 A369601 A369602 * A369604 A369605 A369606

KEYWORD

base,nonn

AUTHOR

Eric Angelini and Giorgos Kalogeropoulos, Jan 27 2024

STATUS

approved