A330290 a(1) = 1; for n > 1, a(n) = the smallest divisor of the number formed by the concatenation of a(1) to a(n-1) that has not previously appeared in the sequence.

1, 1, 11, 101, 3, 9, 7, 61, 1821477701, 311, 449, 89, 29, 37, 121, 349, 1047, 73, 2741, 59, 5527, 21, 487, 3679724250117316595527, 137, 257, 33, 99, 27, 47, 17, 19, 13, 39, 63, 23, 557, 53, 159, 117, 351, 81, 3439913, 677, 83, 197, 151, 453, 211, 1033, 239296537198126662281, 167, 501

Offset

1,3

Comments

The next term a(54) requires the factorization of a composite 177 digit number 22177...67001.

Links

Table of n, a(n) for n=1..53.

Example

a(3) = 11 as the concatenation of a(1) and a(2) = '11' and 11, the smallest divisor of 11, has not appeared in the sequence.
a(4) = 101 as the concatenation of a(1)..a(3) is '1111' and 101 is the smallest divisor of 1111 which has not appeared in the sequence. Note that 11 also divides 1111 but a(3) = 11.
a(6) = 9 as the concatenation of a(1)..a(5) is '11111013' and 9 is the smallest divisor of 11111013 which has not appeared in the sequence. Note that 3 also divides 11111013 but a(5) = 3.

Crossrefs

Cf. A020639, A000040, A000005, A330291, A330293, A240588.

Sequence in context: A266515 A036929 A168586 * A330291 A318647 A185121

Adjacent sequences: A330287 A330288 A330289 * A330291 A330292 A330293

Keyword

nonn,more,hard,base

Author

Scott R. Shannon, Dec 09 2019

Status

approved