A057227 Smallest member of smallest set S(n) of positive integers containing n which satisfies "k is in S, iff 2k-1 is in S, iff 4k is in S".

1, 2, 2, 1, 2, 6, 1, 2, 2, 10, 6, 2, 1, 14, 2, 1, 2, 18, 10, 2, 6, 22, 2, 6, 1, 26, 14, 1, 2, 30, 1, 2, 2, 34, 18, 2, 10, 38, 2, 10, 6, 42, 22, 6, 2, 46, 6, 2, 1, 50, 26, 1, 14, 54, 1, 14, 2, 58, 30, 2, 1, 62, 2, 1, 2, 66, 34, 2, 18, 70, 2, 18, 10, 74, 38, 10, 2, 78, 10, 2, 6, 82, 42, 6, 22

Offset: 1

Author

Henry Bottomley, Nov 23 2000

Keywords

• nonn

Comments

Ratio of number of times 2 appears to number of times 1 appears tends towards (1+sqrt(5))/2. Ratio of number of times 2 appears to number of times 4m+2 appears tends towards ((1+sqrt(5))/2)^log_2(2m+1).

Examples

			a(23)=2 since if 23 is in S(23) then so are 12, 3 and 2; however 1 need not be and so the smallest member of S(23) is 2.
		

Links

• Michael Gilleland, Some Self-Similar Integer Sequences

Crossrefs

All values of a(n) are 1 or of form 4m+2, i.e., A016825. a(n)=1 iff n is in A048297.