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%I #20 Feb 12 2024 02:06:39
%S 4,44,484,48884,8408048,84088888048,8408888888888888048,
%T 84088888888888888888888888888888048
%N a(1) = 4, a(n) = smallest palindromic nontrivial multiple of a(n-1) containing all decimal digits of a(n-1).
%C Differs from A082779 at a(5).
%C a(n) <= (10^A055642(a(n-1))+1)*a(n-1).
%C 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).
%C 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
%e a(3) = 484 is a palindromic multiple of a(2) = 44 and contains two '4', all the digits of a(2).
%Y Cf. A055642, A082779, A370052, A370053.
%K nonn,base,more
%O 1,1
%A _Chai Wah Wu_, Mar 08 2021
%E a(8) from _Max Alekseyev_, Feb 07 2024
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