cp's OEIS Frontend

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.

%I A093782 #17 Oct 19 2017 10:43:04
%S A093782 5,0,17,19,127,61,2,31,97,13,23,269,53,239,181,449,541,11,953,1741,
%T A093782 179,1889,823,3209,13619,383,6971,10331,45959,13721
%N 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.
%C A093782 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.
%C A093782 a(31)>=8581. [_Sean A. Irvine_, Oct 31 2011]
%e A093782 The sequence for 17 is 17, 2, 5, ... where the 5 is at the third place, therefore a(3)=17.
%e A093782 For n=15 we have the sequence 181, 2, 3, 1087, 73, 7, 29, 151, 61, 98689, 11, 10929259909, 678859, 97, 5, ...
%e A093782 a(16) = 449 uses the sequence 449, 2, 29, 3, 7, 349, 190861819, 166273, 16091, 11, 3807491, 53, 17, 313, 23, 5, ...
%e A093782 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.
%Y A093782 Cf. A000945, A051308-A051334, A056756, A093777-A093781.
%K A093782 more,nonn
%O A093782 1,1
%A A093782 _Labos Elemer_, May 04 2004
%E A093782 Corrected by _R. J. Mathar_, Oct 06 2006
%E A093782 a(16) = 449 was conjectured by _R. J. Mathar_ and confirmed by _Don Reble_, Oct 07 2006
%E A093782 a(19)-a(24) from _David Wasserman_, Apr 20 2007
%E A093782 a(25)-a(30) from _Sean A. Irvine_, Oct 30 2011