A342346 a(1) = 4, a(n) = smallest palindromic nontrivial multiple of a(n-1) containing all decimal digits of a(n-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

Links

Table of n, a(n) for n=1..8.

Example

a(3) = 484 is a palindromic multiple of a(2) = 44 and contains two '4', all the digits of a(2).

Crossrefs

Cf. A055642, A082779, A370052, A370053.

Sequence in context: A112897 A163013 A087813 * A082779 A223053 A222288

Adjacent sequences: A342343 A342344 A342345 * A342347 A342348 A342349

Keyword

nonn,base,more

Author

Chai Wah Wu, Mar 08 2021

Extensions

a(8) from Max Alekseyev, Feb 07 2024

Status

approved