A093782 a(n) is the smallest initial value (a prime) for the Euclid-Mullin (EM) sequence in which the p=5 prime emerges as n-th term, i.e., arises at the n-th position.

5, 0, 17, 19, 127, 61, 2, 31, 97, 13, 23, 269, 53, 239, 181, 449, 541, 11, 953, 1741, 179, 1889, 823, 3209, 13619, 383, 6971, 10331, 45959, 13721

Offset

1,1

Comments

The sequence is not monotonic and it seems that p=5 may arise at any position > 2. a(2)=0 means that 5 is never the 2nd term in an EM sequence of A000945-type because a(2)=2 or 3.

a(31)>=8581. [Sean A. Irvine, Oct 31 2011]

Links

Table of n, a(n) for n=1..30.

Example

The sequence for 17 is 17, 2, 5, ... where the 5 is at the third place, therefore a(3)=17.
For n=15 we have the sequence 181, 2, 3, 1087, 73, 7, 29, 151, 61, 98689, 11, 10929259909, 678859, 97, 5, ...
a(16) = 449 uses the sequence 449, 2, 29, 3, 7, 349, 190861819, 166273, 16091, 11, 3807491, 53, 17, 313, 23, 5, ...
The sequence for 11 is 11, 2, 23, 3, 7, 13, 10805892983887, 73, 6397, 19, 489407, 2753, 87491, 18618443, 5, ... with the 5 at the 18th place, so a(18)=11.

Crossrefs

Cf. A000945, A051308-A051334, A056756, A093777-A093781.

Sequence in context: A321416 A226372 A367191 * A085105 A368061 A094031

Adjacent sequences: A093779 A093780 A093781 * A093783 A093784 A093785

Keyword

more,nonn

Author

Labos Elemer, May 04 2004

Extensions

Corrected by R. J. Mathar, Oct 06 2006

a(16) = 449 was conjectured by R. J. Mathar and confirmed by Don Reble, Oct 07 2006

a(19)-a(24) from David Wasserman, Apr 20 2007

a(25)-a(30) from Sean A. Irvine, Oct 30 2011

Status

approved