A337498 a(0) = 0; for n>0, a(n) = the smallest positive integer m not yet in the sequence with property that none of the numbers in row m of A193829 have occurred previously in the sequence.

0, 2, 5, 6, 11, 13, 17, 18, 23, 25, 29, 31, 37, 41, 42, 47, 53, 54, 59, 61, 65, 67, 71, 73, 79, 83, 85, 89, 95, 97, 101, 103, 107, 109, 113, 121, 125, 127, 131, 137, 139, 145, 149, 151, 155, 157, 162, 167, 169, 173, 179, 181, 185, 191, 193, 197, 199, 205, 209, 211, 215, 221, 223, 227, 229

Offset

0,2

Comments

The vast majority of terms are odd - in the first one million terms only 74 even numbers appear. Interestingly most of those even number appear in A014741, although that sequence contains many even numbers that do not appear here, e.g. 126, while this sequence contains even numbers not appearing in that sequence, e.g. 326.

Links

Table of n, a(n) for n=0..64.

Example

a(1) = 2 as the consecutive divisors of 2 are 1,2 the difference of which is 1, which has not occurred previously in the sequence.
a(2) = 5. The consecutive divisors of 3 are 1,3, the difference of which is 2, but a(1) = 2 so 3 cannot appear. The consecutive divisors of 4 are 1,2,4, the differences of which are 1,2, but a(1) = 2 so 4 cannot appear. The consecutive divisors of 5 are 1,5, the difference of which is 4 and as 4 has not occurred previously in the sequence a(2) = 5.
a(3) = 6 as the consecutive divisors of 6 are 1,2,3,6, the differences of which are 1,1,3, and as neither 1 or 3 has occurred previously a(3) = 6.
a(4) = 11. The divisors of 7 are 1,7 with a difference of 6, the divisors of 8 are 1,2,4,8 with differences 1,2,4, the divisors of 9 are 1,3,9 with differences 2,6, and the divisors of 10 are 1,2,5,10, with differences 1,3,5. All of 6,2,2,5 have all occurred previously in the sequence. The divisors of 11 are 1,11 with a difference of 10, which has not occurred previously so a(4) = 11.

Crossrefs

Cf. A027750, A193829, A014741.

Sequence in context: A328893 A030130 A164874 * A045845 A002133 A092306

Adjacent sequences: A337495 A337496 A337497 * A337499 A337500 A337501

Keyword

nonn

Author

Scott R. Shannon, Sep 26 2020

Status

approved