A392142 Starting with a(1) = 1, each term is obtained by doubling the previous term and then deleting repeated digits, keeping only the first occurrence of each digit.

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 653, 1306, 261, 52, 104, 208, 416, 832, 164, 328, 65, 130, 260, 520, 104, 208, 416, 832, 164, 328, 65, 130, 260, 520, 104, 208, 416, 832, 164, 328, 65, 130, 260, 520, 104, 208, 416, 832, 164, 328, 65, 130, 260, 520

Offset

1,2

Comments

Periodic with period 10 beginning at a(21) = 104.

Links

Table of n, a(n) for n=1..60.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,1).

Formula

a(n) = A137564(2*a(n-1)).

a(n) = a(n-10) for n >= 31.

Example

For n = 17 we have that 32768 * 2 = 65536, so a(17) = 653.
For n = 18 we have that 653 * 2 = 1306, so a(18) = 1306.
For n = 19 we have that 1306 * 2 = 2612, so a(19) = 261.

Mathematica

a[n_] := a[n] = FromDigits[DeleteDuplicates[IntegerDigits[2*a[n-1]]]]; a[1] = 1; Array[a, 60] (* Amiram Eldar, Jan 01 2026 *)

Prog

(Python)
from itertools import islice
def f(n): # A137564
    seen, out, s = set(), "", str(n)
    for d in s:
        if d not in seen: out += d; seen.add(d)
    return int(out)
def A392142(): # generator of terms
    an = 1
    while True:
        yield an
        an = f(2*an)
print(list(islice(A392142(), 60))) # Michael S. Branicky, Jan 01 2026

Crossrefs

Cf. A137564, A370748.

Sequence in context: A220493 A320487 A323830 * A370748 A118655 A335891

Adjacent sequences: A392139 A392140 A392141 * A392143 A392144 A392145

Keyword

nonn,base,easy

Author

Rodolfo Kurchan, Jan 01 2026

Status

approved