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

Author

Sergio Pimentel, Mar 07 2024

Keywords

• base
• nonn

Comments

Duplicate digits are eliminated as in A137564.

No term can be greater than 9876543210.

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

Examples

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

Links

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

Crossrefs

Cf. A010784, A137564, A370254.

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

Programs

Mathematica

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

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