OFFSET
0,2
COMMENTS
Equivalently, a(n) is the smallest base-10 palindrome of the form (2k+1)*2^n.
Conjecture: a(n) > 0 for all n >= 0.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 0..40
FORMULA
If A082613(n)/A082614(n) = 2^n (see conjecture at A082613) and a(n) > 0, then a(n) >= A082613(n). - Altug Alkan, Apr 15 2018
EXAMPLE
n a(n) binary expansion of a(n)
== ============= ==========================================
0 1 1
1 2 10
2 4 100
3 8 1000
4 272 100010000
5 25952 110010101100000
6 2112 100001000000
7 4224 1000010000000
8 8448 10000100000000
9 44544 1010111000000000
10 2532352 1001101010010000000000
11 6547456 11000111110100000000000
12 405504 1100011000000000000
13 236101632 1110000100101010000000000000
14 8634368 100000111100000000000000
15 487030784 11101000001111000000000000000
16 677707776 101000011001010000000000000000
17 61486268416 111001010000110111100000000000000000
18 25135153152 10111011010001011000000000000000000
19 4285005824 11111111011010000000000000000000
20 2912594952192 101010011000100100001100000000000000000000
PROG
(PARI) isp(n) = n=digits(n); for(i=1, #n\2, if(n[i]!=n[#n+1-i], return(0))); 1;
a(n) = forstep(k=1, oo, 2, if(isp(p=k*2^n), return(p))); \\ Altug Alkan, Apr 15 2018, after Charles R Greathouse IV at A002113
(Python)
from itertools import count
def A302864(n):
for k in count(0, 2):
if (s:=str(k+1<<n))[:(t:=(len(s)+1)//2)]==s[:-t-1:-1]:
return k+1<<n # Chai Wah Wu, Jun 23 2022
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Jon E. Schoenfield, Apr 14 2018
EXTENSIONS
a(26) from Chai Wah Wu, Mar 06 2019
STATUS
approved