A370748 a(0)=1; a(n) = sum of all previous terms, eliminating repeated digits (starting from the left).

1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 653, 6189, 7238, 7961, 875, 8452, 9604, 10658, 176, 17342, 13468, 14852, 16304, 179308, 35861, 3947, 39842, 43826, 48209, 5301, 53602, 589204, 17840, 196248, 139246, 153742, 16854

Offset

0,3

Comments

Duplicate digits are eliminated as in A137564.

No term can be greater than 9876543210.

a(260390084) = 9876543210. - Michael S. Branicky, Apr 09 2024

Links

Alois P. Heinz, Table of n, a(n) for n = 0..20000

Example

a(17) = 653 since the sum of a(0) through a(16) is 65536, and eliminating repeated digits gives a(17) = A137564(65536) = 653.

Mathematica

seq={1}; Do[s=Total[seq]; AppendTo[seq, FromDigits[DeleteDuplicates[IntegerDigits[s]]]], 43]; seq (* James C. McMahon, Apr 09 2024 *)

Prog

(PARI) f(n) = my(d=digits(n)); fromdigits(vecextract(d, vecsort(vecsort(d, , 9)))) \\ A137564
lista(nn) = my(va=vector(nn)); va[1] = 1; for (n=2, nn, va[n] = f(sum(j=1, n-1, va[j])); ); va; \\ Michel Marcus, Mar 08 2024
(Python)
from itertools import islice
def A137564(n):
    seen, out, s = set(), "", str(n)
    for d in s:
        if d not in seen: out += d; seen.add(d)
    return int(out)
def A370748gen(): # generator of terms
    an, s = 1, 0
    while True:
        yield an
        s += an
        an = A137564(s)
print(list(islice(A370748gen(), 45))) # Michael S. Branicky, Apr 09 2024

Crossrefs

Cf. A010784, A137564, A370254.

Cf. A371863 (records), A371864 (indices of records).

Sequence in context: A220493 A320487 A323830 * A118655 A335891 A249169

Adjacent sequences: A370745 A370746 A370747 * A370749 A370750 A370751

Keyword

base,nonn

Author

Sergio Pimentel, Mar 07 2024

Status

approved