|
%I #16 Aug 02 2019 23:08:03
%S 1,2,4,8,16,20,44,92,110,136,152,170,172,188,200,212,236,242,256,272,
%T 316,332,368,440,488,500,590,616,620,632,650,676,704,710,742,788,824,
%U 848,892,946,952,968,1010,1034,1036,1052,1058,1088,1118
%N Let S(k) be the sequence s() defined by s(1) = k; for i > 1, s(i) = s(i-1) + gcd(s(i-1), i). Start with the list of positive integers and remove any k's for which S(k) merges with an S(m) with m < k. Each value k > 1 is conjectural.
%C For the given initial values k, it is conjectural that their sequences S(k) never merge. The S(k) have been checked to be distinct for 2^60 terms (see Rowland link), but it is possible that they merge later on.
%H Eric Rowland, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL11/Rowland/rowland21.html">A Natural Prime-Generating Recurrence</a> (Section 5: Primes), Journal of Integer Sequences, Vol. 11 (2008), Article 08.2.8.
%e From _Danny Rorabaugh_, Apr 02 2015: (Start)
%e S(1) = A000027 is the positive integers.
%e S(2) = [2,4,5,...,i+2,...].
%e S(3) = [3,4,5,...,i+2,...] merges with S(2) at index 2.
%e S(4) = [4,6,9,10,15,18,19,20,21,22,33,...] = A084662.
%e S(5) = [5,6,9,...] = A134736 merges with S(4) at index 2.
%e (End)
%Y Cf. A000027 (S(1)), A084662 (S(4)), A134736 (S(5)), A106108 (S(7)), A084663 (S(8)).
%Y Cf. A106108 for other Crossrefs.
%K nonn
%O 1,2
%A _Eric Rowland_, Jan 29 2008
|
