A305396 Records in A171797 starting from a(1).

101, 110, 211, 220, 321, 330, 431, 440, 541, 550, 651, 660, 761, 770, 871, 880, 981, 990, 1091, 10010, 10100, 11101, 11110, 12111, 12210, 13121, 13310, 14131, 14410, 15141, 15510, 16151, 16610, 17161, 17710, 18171, 18810, 19181, 19910, 20191, 201010, 211110

Offset

1,1

Comments

The record-holders are the powers of 2 written in base 4, A004643.

Not all record terms of A171797 have index in A004643. For instance, a(20) = 10010 = A171797(1111111111). - 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

M. E. Coppenbarger, Iterations of a modified Sisyphus function, Fib. Q., 56 (No. 2, 2018), 130-141.

Prog

(Python)
from itertools import count, islice
def A305396_gen(): # generator of terms
    c = 0
    for n in count(1):
        m = int(str(l:=len(s:=str(n)))+str(e:=sum(1 for d in s if d in {'0', '2', '4', '6', '8'}))+str(l-e))
        if m>c:
            yield m
            c = m
A305396_list = list(islice(A305396_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(s+str(k-i)+str(i))
        yield int(s*2+'0') # no odd digit
def A305396_gen():
    M = 0
    for x in candidate_values():
        if x > M:
            yield x
            M = x # Pontus von Brömssen, Jan 14 2026

Crossrefs

Cf. A171797, A004643.

Sequence in context: A025341 A290725 A255966 * A266717 A303571 A303573

Adjacent sequences: A305393 A305394 A305395 * A305397 A305398 A305399

Keyword

nonn,base

Author

N. J. A. Sloane, Jun 25 2018

Extensions

a(11)-a(23) from Chai Wah Wu, Nov 19 2025

a(24)-a(27) from Chai Wah Wu, Jan 13 2026

a(28)-a(42) from Pontus von Brömssen, Jan 14 2026

Status

approved