A109326 Smallest positive number that requires n steps to be represented as a sum of palindromes using the greedy algorithm.

1, 10, 21, 1022, 101023, 1000101024

Offset: 1

Author

David Wasserman, Aug 11 2005

Keywords

• nonn
• base
• more

Comments

Index of first occurrence of n in A088601.

Presumably this sequence is unbounded. - N. J. A. Sloane, Aug 28 2015

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

Links

• M. F. Hasler, Sum of palindromes, OEIS wiki, Sept. 2015.

Crossrefs

Cf. A088601, A002113, A261422, A261423.

Programs

Python

# uses functions in A088601
def afind(limit):
    record = 0
    for i in range(1, limit+1):
        steps = A088601(i)
        if steps > record: print(i, end=", "); record = steps
afind(10**6) # Michael S. Branicky, Jul 12 2021

Formula

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

Extensions

Edited by N. J. A. Sloane, Aug 28 2015