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A342346
a(1) = 4, a(n) = smallest palindromic nontrivial multiple of a(n-1) containing all decimal digits of a(n-1).
1
4, 44, 484, 48884, 8408048, 84088888048, 8408888888888888048, 84088888888888888888888888888888048
OFFSET
1,1
COMMENTS
Differs from A082779 at a(5).
a(n) <= (10^A055642(a(n-1))+1)*a(n-1).
If a(n-1) > 10 and the last digit of a(n-1) <= 4, then a(n) <= (10^(A055642(a(n-1))-1)+1)*a(n-1).
For n = 5..8, we have a(n) = 7568 * A002275(2^(n-3)), and it follows that a(9) <= 7568 * A002275(64). Conjecture: for all n >= 5, a(n) = 7568 * A002275(2^(n-3)). Note that 7568 is a term of A370052 and A370053. - Max Alekseyev, Feb 08 2024
EXAMPLE
a(3) = 484 is a palindromic multiple of a(2) = 44 and contains two '4', all the digits of a(2).
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Chai Wah Wu, Mar 08 2021
EXTENSIONS
a(8) from Max Alekseyev, Feb 07 2024
STATUS
approved