A134162 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.

1, 2, 4, 8, 16, 20, 44, 92, 110, 136, 152, 170, 172, 188, 200, 212, 236, 242, 256, 272, 316, 332, 368, 440, 488, 500, 590, 616, 620, 632, 650, 676, 704, 710, 742, 788, 824, 848, 892, 946, 952, 968, 1010, 1034, 1036, 1052, 1058, 1088, 1118

Offset: 1

Author

Eric Rowland, Jan 29 2008

Keywords

• nonn

Comments

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.

Examples

			From _Danny Rorabaugh_, Apr 02 2015: (Start)
S(1) = A000027 is the positive integers.
S(2) = [2,4,5,...,i+2,...].
S(3) = [3,4,5,...,i+2,...] merges with S(2) at index 2.
S(4) = [4,6,9,10,15,18,19,20,21,22,33,...] = A084662.
S(5) = [5,6,9,...] = A134736 merges with S(4) at index 2.
(End)
		

Links

• Eric Rowland, A Natural Prime-Generating Recurrence (Section 5: Primes), Journal of Integer Sequences, Vol. 11 (2008), Article 08.2.8.

Crossrefs

Cf. A000027 (S(1)), A084662 (S(4)), A134736 (S(5)), A106108 (S(7)), A084663 (S(8)).

Cf. A106108 for other Crossrefs.