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A369899
a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest unused positive number that is a substring of the sum of all previous terms.
2
1, 2, 3, 6, 12, 4, 8, 36, 7, 9, 88, 17, 19, 21, 23, 5, 26, 28, 15, 30, 60, 20, 40, 48, 52, 58, 38, 67, 43, 78, 64, 92, 10, 103, 11, 14, 115, 27, 13, 31, 34, 37, 41, 45, 50, 51, 16, 18, 63, 69, 68, 83, 91, 201, 22, 33, 66, 32, 236, 260, 86, 29, 75, 305, 35, 39, 42, 47, 351, 386, 25, 80, 360, 72
OFFSET
1,2
COMMENTS
The fixed points begin 1, 2, 3, 94, 1420, 1423, 1425, 1426, 1427, 8592, although it is likely there are infinitely more. The sequence is conjectured to be a permutation of the positive numbers.
LINKS
EXAMPLE
a(6) = 4 as the sum of all previous terms is 1 + 2 + 3 + 6 + 12 = 24, and 4 is the smallest unused number that is a substring of "24".
PROG
(Python)
from itertools import islice
def agen(): # generator of terms
s, mink, aset = 3, 3, {1, 2}
yield from [1, 2]
while True:
an, ss = mink, str(s)
while an in aset or not str(an) in ss: an += 1
aset.add(an); s += an; yield an
while mink in aset: mink += 1
print(list(islice(agen(), 74))) # Michael S. Branicky, Feb 08 2024
CROSSREFS
Cf. A370046 (base 2), A363186, A333410.
Sequence in context: A358237 A294720 A082002 * A102779 A287109 A084417
KEYWORD
nonn,look,base
AUTHOR
Scott R. Shannon, Feb 05 2024
STATUS
approved