A389594 a(1) = 1; a(n+1) = a(n)-th positive integer that is not a power of 2.

1, 3, 6, 10, 14, 19, 24, 29, 35, 41, 47, 53, 59, 66, 73, 80, 87, 94, 101, 108, 115, 122, 130, 138, 146, 154, 162, 170, 178, 186, 194, 202, 210, 218, 226, 234, 242, 250, 259, 268, 277, 286, 295, 304, 313, 322, 331, 340, 349, 358, 367, 376, 385, 394, 403, 412, 421

Offset

1,2

Comments

a(n) = A130235(n-1) + 1 for n<=21.

Links

Dmitry Yampolsky, Table of n, a(n) for n = 1..10000

Kevin Ryde, PARI/GP Code

Formula

a(n) = A057716(a(n-1)).

Mathematica

k=100; n=Complement[Range@k, 2^Range[0, Floor@Log2@k]];
a=NestWhileList[n[[#]]&, 1, #<=Length@n&];
TableForm@Transpose@{Range@Length@a, a}

Prog

(Python)
from itertools import islice
def A057716(n): return n+(k:=n.bit_length())+(n+k>=1<<k)
def A389594_gen(): # generator of terms
    yield (a:=1)
    while True:
        yield (a:=A057716(a))
A389594_list = list(islice(A389594_gen(), 30)) # Chai Wah Wu, Nov 18 2025
(PARI) \\ See links.

Crossrefs

Cf. A057716, A130235.

Cf. A088236, A025003, A056875.

Sequence in context: A259646 A310069 A310070 * A036572 A139328 A253620

Adjacent sequences: A389591 A389592 A389593 * A389595 A389596 A389597

Keyword

nonn

Author

Dmitry Yampolsky, Nov 10 2025

Status

approved