A109326 - OEIS

%I #39 Oct 05 2021 05:06:31

%S 1,10,21,1022,101023,1000101024

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

%C Index of first occurrence of n in A088601.

%C Presumably this sequence is unbounded. - _N. J. A. Sloane_, Aug 28 2015

%C 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^(n-2) + 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

%H M. F. Hasler, <a href="/wiki/User:M._F._Hasler/Work_in_progress/Sum_of_palindromes">Sum of palindromes</a>, OEIS wiki, Sept. 2015.

%F a(n) = Sum_{0 <= k <= n-3} 10^(2^k+1) + n - 82, for n > 2 (conjectured). - _M. F. Hasler_, Sep 08 2015

%o (Python) # uses functions in A088601

%o def afind(limit):

%o     record = 0

%o     for i in range(1, limit+1):

%o         steps = A088601(i)

%o         if steps > record: print(i, end=", "); record = steps

%o afind(10**6) # _Michael S. Branicky_, Jul 12 2021

%Y Cf. A088601, A002113, A261422, A261423.

%K nonn,base,more

%O 1,2

%A _David Wasserman_, Aug 11 2005

%E Edited by _N. J. A. Sloane_, Aug 28 2015