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URL: https://oeis.org/A305395

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A305395
Records in A073053 starting from a(1).
3
11, 101, 112, 202, 213, 303, 314, 404, 415, 505, 516, 606, 617, 707, 718, 808, 819, 909, 9110, 10010, 10111, 11011, 11112, 21012, 31013, 41014, 51015, 61016, 71017, 81018, 91019, 101020, 111021, 121022, 131023, 141024, 151025, 161026, 171027, 181028, 191029
OFFSET
1,1
COMMENTS
The record-holders are the powers of 2 written in base 4, A004643.
Not all record terms of A073053 have index in A004643. For instance, a(22) = 11011 = A073053(10111111111). - Chai Wah Wu, Nov 19 2025
All record-holders are of one of the forms 2*10^k or 10^k+(10^j-1)/9 with 0 <= j <= k. - Pontus von Brömssen, Jan 14 2026
LINKS
Pontus von Brömssen, Table of n, a(n) for n = 1..10000
Matthew E. Coppenbarger, Iterations of a modified Sisyphus function, Fib. Q., 56 (No. 2, 2018), 130-141.
PROG
(Python)
from itertools import count, islice
def A305395_gen(): # generator of terms
c = 0
for n in count(1):
l = len(s:=str(n))
m = int(str(e:=sum(1 for d in s if d in {'0', '2', '4', '6', '8'}))+str(l-e)+str(l))
if m>c:
yield m
c = m
A305395_list = list(islice(A305395_gen(), 15)) # Chai Wah Wu, Nov 19 2025
(Python)
from itertools import count
def candidate_values():
for k in count(1): # number of digits in record-holder candidates
s = str(k)
for i in range(1, k+1): # number of odd digits
yield int(str(k-i)+str(i)+s)
yield int(s+'0'+s) # no odd digit
def A305395_gen():
M = 0
for x in candidate_values():
if x > M:
yield x
M = x # Pontus von Brömssen, Jan 14 2026
CROSSREFS
Sequence in context: A247647 A240602 A117697 * A158051 A091366 A073064
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Jun 25 2018
EXTENSIONS
a(11)-a(22) from Chai Wah Wu, Nov 19 2025
a(23)-a(25) from Chai Wah Wu, Jan 13 2026
a(26)-a(41) from Pontus von Brömssen, Jan 14 2026
STATUS
approved