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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.
5
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
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
KEYWORD
base,nonn
AUTHOR
STATUS
approved