

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.


5



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
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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.


MAPLE

with(numtheory):
T:=proc(t) local x, y; x:=t; y:=0; while x>0 do x:=trunc(x/10); y:=y+1; od; end:
P:=proc(q) local a, b, c, k, n; b:=21; print(2); print(1); c:=[1, 2];
for n from 1 to q do a:=sort([op(divisors(b))]); for k from 2 to nops(a) do
if not member(a[k], c) then c:=[op(c), a[k]]; b:=a[k]+b*10^T(a[k]); print(a[k]); break;
fi; od; od; end: P(30); # Paolo P. Lava, Apr 29 2014


CROSSREFS

Cf. A096097.
Sequence in context: A059333 A106485 A126008 * A096097 A212805 A246431
Adjacent sequences: A096095 A096096 A096097 * A096099 A096100 A096101


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



