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A247243
a(n) = smallest positive integer k not already in the sequence such that the decimal expansion of 2^(n-1) begins with k.
2
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?
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: A050124 A101943 A331440 * A341819 A352387 A110001
KEYWORD
nonn,base
AUTHOR
Paul Tek, Nov 30 2014
STATUS
approved