A342347 a(1) = 7, a(n) = smallest palindromic nontrivial multiple of a(n-1) containing all decimal digits of a(n-1).

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

Links

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

Example

a(3) = 1771 is a palindromic multiple of a(2) = 77 and contains two '7', all the digits of a(2).

Crossrefs

Cf. A055642, A082782, A342232, A342233, A342345, A342346, A370052, A370053.

Sequence in context: A093980 A077706 A080492 * A082782 A356437 A107047

Adjacent sequences: A342344 A342345 A342346 * A342348 A342349 A342350

Keyword

nonn,base,more

Author

Chai Wah Wu, Mar 08 2021

Extensions

a(8) from Max Alekseyev, Feb 15 2024

Status

approved