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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 18 00:21 EDT 2019. Contains 328135 sequences. (Running on oeis4.)