

A109326


Smallest positive number that requires n steps to be represented as a sum of palindromes using the greedy algorithm.


3




OFFSET

1,2


COMMENTS

Index of first occurrence of n in A088601.
The greedy algorithm means iteration of A261424 until a palindrome is reached. For n = 3, 4, ... we have a(n+1) = 10^L(n) + a(n) + 1 with L(n) = 2^(n2) + 1 = length(a(n))*2  3 for n > 3. We have a(7) <= 10^17 + 1000101025, a(8) <= 10^33 + 10^17 + 1000101026, a(9) <= 10^65 + 10^33 + 10^17 + 1000101027, a(10) <= 10^129 + 10^65 + 10^33 + 10^17 + 1000101028, etc, with conjectured equality.  M. F. Hasler, Sep 08 2015, edited Sep 09 2018


LINKS



FORMULA

a(n) = Sum_{0 <= k <= n3} 10^(2^k+1) + n  82, for n > 2 (conjectured).  M. F. Hasler, Sep 08 2015


PROG

(Python) # uses functions in A088601
def afind(limit):
record = 0
for i in range(1, limit+1):
if steps > record: print(i, end=", "); record = steps


CROSSREFS



KEYWORD

nonn,base,more


AUTHOR



EXTENSIONS



STATUS

approved



