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A109326 Smallest positive number that requires n steps to be represented as a sum of palindromes using the greedy algorithm. 3
1, 10, 21, 1022, 101023, 1000101024 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
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.
FORMULA
a(n) = Sum_{0 <= k <= n-3} 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):
steps = A088601(i)
if steps > record: print(i, end=", "); record = steps
afind(10**6) # Michael S. Branicky, Jul 12 2021
CROSSREFS
Sequence in context: A041198 A035318 A039821 * A369120 A080454 A226789
KEYWORD
nonn,base,more
AUTHOR
David Wasserman, Aug 11 2005
EXTENSIONS
Edited by N. J. A. Sloane, Aug 28 2015
STATUS
approved

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Last modified July 20 12:30 EDT 2024. Contains 374445 sequences. (Running on oeis4.)