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A109326
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Smallest positive number that requires n steps to be represented as a sum of palindromes using the greedy algorithm.
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3
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OFFSET
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1,2
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COMMENTS
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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^(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
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LINKS
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FORMULA
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a(n) = Sum_{0 <= k <= n-3} 10^(2^k+1) + n - 82, for n > 2 (conjectured). - M. F. Hasler, Sep 08 2015
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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