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URL: https://oeis.org/A342347

⇱ A342347 - OEIS

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A342347
a(1) = 7, a(n) = smallest palindromic nontrivial multiple of a(n-1) containing all decimal digits of a(n-1).
0
7, 77, 1771, 178871, 1788888871, 2188118778118812, 218811879999999978118812, 2188118799999999999999999999999978118812
OFFSET
1,1
COMMENTS
Differs from A082782 at a(6).
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=6..8, a(n) = 196930692 * A002275(2^(n-3)), and it follows that a(9) <= 196930692 * A002275(64). Conjecture: for all n >= 6, a(n) = 196930692 * A002275(2^(n-3)). Note that 196930692 is a term of A370052 and A370053. - Max Alekseyev, Feb 15 2024
EXAMPLE
a(3) = 1771 is a palindromic multiple of a(2) = 77 and contains two '7', all the digits of a(2).
KEYWORD
nonn,base,more
AUTHOR
Chai Wah Wu, Mar 08 2021
EXTENSIONS
a(8) from Max Alekseyev, Feb 15 2024
STATUS
approved