A096098 a(1) = 2, a(2) = 1; for n >= 3, a(n) = least number not included earlier that divides the concatenation of all previous terms.

2, 1, 3, 71, 7, 21, 599, 173, 11, 23, 161, 49, 13, 9, 131, 19, 33, 17, 1489, 331, 3989, 69, 3097350956401900335673788279883089441874368101, 349387, 5651, 443, 29, 51, 479470832244949, 661, 1129, 1873, 181, 1544577973887516219070997863, 521

Offset: 1

Author

Amarnath Murthy, Jun 24 2004

Keywords

• base
• nonn

Comments

Conjecture (1) Every concatenation is squarefree.

Conjecture (2) This is a rearrangement of the squarefree numbers not divisible by 5. False! (The a(n) are not always squarefree, since a(12)=49 and a(14)=9.)

Fact: All a(n) for n >= 2 are odd, since a(2) = 1 and odd a(n) => odd concatenation => odd a(n+1). - Wolfdieter Lang, May 08 2014 (editing an earlier statement).

Conjecture (3) the sequence for n>=2 is a permutation of the positive integers not divisible by 2 or 5.

a(29) is probably 479470832244949, in which case the sequence continues 479470832244949, 661, 1129, 1873, 181. - Martin Fuller, Nov 21 2007

Factorization for a(29): 479470832244949*3*17*43217123024009614997922599713504735424547343*P51. - Sean A. Irvine, May 25 2010

Assuming Conjecture (3), the smallest number yet to appear is 89. - Sean A. Irvine, May 11 2014

The factorization given by Sean A. Irvine above is not for the prime a(29) = 479470832244949 but for the concatenation of a(1), a(2), ..., a(29), and P51 means a prime with 51 digits, namely 202232656574589264871780464738430216507933940172343. - Wolfdieter Lang, May 11 2014

Examples

			a(6) = 21 as 213717 = 3*7*10177, and 3 = a(3) and 7 = a(4), hence 3*7 = 21 is the least number dividing 213717 not included earlier in the sequence.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..172
• Sean A. Irvine, Factorizations, for n = 1..182

Crossrefs

Cf. A096097.

Extensions

More terms from R. J. Mathar, Aug 03 2007

a(23)-a(26) from N. J. A. Sloane, Nov 10 2007

Corrected and extended by Martin Fuller, Nov 21 2007

More terms from Sean A. Irvine, May 25 2010

Example detailed. - Wolfdieter Lang, May 08 2014