A076087 a(n) = 7*n - 3 * Sum_{i=1..n} A006460(i).

4, 5, 6, 1, -4, -9, -8, -4, -3, 1, -4, 0, 4, -1, -6, -5, -1, -6, -11, -10, -9, -5, -1, 0, -5, -4, 0, 4, 8, 12, 13, 8, 3, 4, 5, 9, 13, 17, 18, 13, 14, 9, 4, 5, 6, 7, 2, -3, 1, 5, 9, 4, -1, 0, 1, 2, -3, -2, -7, -6, -5, -10, -15, -11, -7, -3, 1, -4, -9, -14, -10, -9, -8, -7, -12, -11, -10, -15, -20, -16, -15, -20, -25, -21, -17, -13, -9

Offset

1,1

Comments

Recalling the Collatz map (cf. A006370 ): x->x/2 if x is even; x->3x+1 if x is odd, let C_m(n) denotes the image of n after m iterations. Then b(n) = A006460(n) = lim_{k -> infinity} C_3k(n) (from the Collatz conjecture C_3k(n) is constant = 1, 2 or 4 for k large enough). Curiously the graph for a(n) presents "regularities" around zero and a pattern coming bigger and bigger. Compared with a random sequence of form : 7*n-3*Sum_{k=1..n} r(k) where r(k) takes random values among (1;2;4).

Links

Table of n, a(n) for n=1..87.

Example

since 3->10->5->16->8->4->2->1 etc. C_6(3)=2 and then for any k>=2 C_3k(3)=2, hence b(3)=2.

Crossrefs

Cf. A006370, A006460.

Sequence in context: A072508 A075566 A348355 * A082486 A106591 A106592

Adjacent sequences: A076084 A076085 A076086 * A076088 A076089 A076090

Keyword

sign

Author

Benoit Cloitre, Oct 30 2002

Extensions

Revised by Sean A. Irvine, Mar 19 2025

Status

approved