OFFSET
1,1
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
LINKS
Sean A. Irvine, Table of n, a(n) for n = 1..172
Sean A. Irvine, Factorizations, for n = 1..182
EXAMPLE
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.
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy, Jun 24 2004
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
STATUS
approved