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.

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

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Scott R. Shannon, Image of the first 50000 terms.

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

Adjacent sequences: A369896 A369897 A369898 * A369900 A369901 A369902

Keyword

nonn,look,base

Author

Scott R. Shannon, Feb 05 2024

Status

approved