A249729 Numbers not fixed by A250249 and A250250.

21, 27, 33, 39, 42, 45, 51, 54, 55, 57, 63, 65, 66, 69, 73, 75, 78, 81, 84, 85, 87, 90, 91, 93, 95, 99, 102, 103, 105, 108, 110, 111, 114, 115, 117, 119, 123, 125, 126, 129, 130, 132, 133, 135, 137, 138, 141, 145, 146, 150, 155, 156, 159, 161, 162, 165, 167, 168, 170, 171, 174, 175, 177, 180, 181, 182, 183, 185, 186, 187, 189, 190, 195, 197, 198, 201

Offset: 1

Author

Antti Karttunen, Nov 18 2014

Keywords

• nonn

Comments

Numbers for which A250249(n) <> n (equally: A250250(n) <> n).

If n is a member, then 2n is also a member. If any 2n is a member, then n is also a member. If n is a member, then the n-th prime, p_n (= A000040(n)) is also a member. If p_n is a member, then its index n is also a member. Thus the sequence is completely determined by its odd nonprime terms: 21, 27, 33, 39, 45, ..., and is obtained as a union of their multiples with powers of 2, and all prime recurrences that start with those values. For example, because 21 is present, then 2*21 = 42 is also present. Furthermore, 73 = p_21 is also present, as well as 367 = p_73 as well as 181 = p_42. See also comments at A250251 and A250249.

Crossrefs

Complement: A250251.

Cf. A000040, A250249, A250250.