A330291 a(1) = 1; for n > 1, a(n) = the smallest prime 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, 17, 65358901, 7, 109, 10193590070216413001, 359, 4007, 149, 43787, 169031777, 67, 13, 14767, 30323, 151651, 1194421, 31008087256045370298219860945197217288544368471059741857398977350440454626775436666667, 1087, 27457, 19301, 23, 22349

Offset

1,3

Comments

The next term a(28) requires the factorization of a composite 195 digit number 49715...700001. Note that for the second term 1 is considered to be prime.

Links

Table of n, a(n) for n=1..27.

Example

a(3) = 11 as the concatenation of a(1) and a(2) = '11' and 11, the smallest prime 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 prime divisor of 1111 which has not appeared in the sequence. Note that 11 also divides 1111 but a(3) = 11.
a(6) = 17 as the concatenation of a(1)..a(5) is '11111013' and 17 is the smallest prime divisor of 11111013 which has not appeared in the sequence. Note that 9 also divides 11111013 and has not appeared but only prime divisors are considered.

Crossrefs

Cf. A020639, A000040, A000005, A330290, A330293, A240588.

Sequence in context: A036929 A168586 A330290 * A318647 A185121 A133835

Adjacent sequences: A330288 A330289 A330290 * A330292 A330293 A330294

Keyword

nonn,more,hard,base

Author

Scott R. Shannon, Dec 09 2019

Status

approved