A247243 a(n) = smallest positive integer k not already in the sequence such that the decimal expansion of 2^(n-1) begins with k.

1, 2, 4, 8, 16, 3, 6, 12, 25, 5, 10, 20, 40, 81, 163, 32, 65, 13, 26, 52, 104, 209, 41, 83, 167, 33, 67, 134, 268, 53, 107, 21, 42, 85, 17, 34, 68, 137, 27, 54, 109, 219, 43, 87, 175, 35, 7, 14, 28, 56, 11, 22, 45, 9, 18, 36, 72, 144, 288, 57, 115, 23, 46, 92

Offset

1,2

Comments

Is this a permutation of the positive integers?

Links

Paul Tek, Table of n, a(n) for n = 1..10000

Paul Tek, Perl program for this sequence

Example

+----+---------+------+
+  n | 2^(n-1) | a(n) |
+----+---------+------+
|  1 |       1 |    1 |
|  2 |       2 |    2 |
|  3 |       4 |    4 |
|  4 |       8 |    8 |
|  5 |      16 |   16 |
|  6 |      32 |    3 |
|  7 |      64 |    6 |
|  8 |     128 |   12 |
|  9 |     256 |   25 |
| 10 |     512 |    5 |
| 11 |    1024 |   10 |
+----+---------+------+

Prog

(Perl) See Link section.
(Python)
from itertools import count, islice
def ispal(n): s = str(n); return s == s[::-1]
def agen(): # generator of terms
    aset, mink = set(), 1
    for n in count(1):
        k, target = mink, str(2**(n-1))
        while k in aset or not target.startswith(str(k)): k += 1
        an = k; aset.add(an); yield an
        while mink in aset: mink += 1
print(list(islice(agen(), 65))) # Michael S. Branicky, Nov 07 2022

Crossrefs

Cf. A008952.

Sequence in context: A101943 A378106 A331440 * A341819 A352387 A110001

Adjacent sequences: A247240 A247241 A247242 * A247244 A247245 A247246

Keyword

nonn,base

Author

Paul Tek, Nov 30 2014

Status

approved