A174978 For definition see comments lines.

1, 2, 1, 5, 2, 2, 1, 20, 2, 5, 2, 5, 2, 2, 1, 95, 2, 5, 2, 20, 2, 5, 2, 20, 2, 5, 2, 5, 2, 2, 1, 470, 2, 5, 2, 20, 2, 5, 2, 95, 2, 5, 2, 20, 2, 5, 2, 95, 2, 5, 2, 20, 2, 5, 2, 20, 2, 5, 2, 5, 2, 2, 1, 2345, 2, 5, 2, 20, 2, 5, 2, 95, 2, 5, 2, 20, 2, 5, 2, 470, 2, 5, 2, 20, 2, 5, 2, 95, 2, 5, 2, 20, 2

Offset

0,2

Comments

It is easier to explain the rule of recurrence when the numbers are written as follows:

1,

2, 1,

5, 2, 2, 1,

20, 2, 5, 2, 5, 2, 2, 1,

95, 2, 5, 2, 20, 2, 5, 2, 20, 2, 5, 2, 5, 2, 2, 1,

470, 2, 5, 2, 20, 2, 5, 2, 95, 2, 5, 2, 20, 2, 5, 2, 95, 2, 5, 2, 20, 2, 5, 2, 20, 2, 5, 2, 5, 2, 2, 1,

2345, 2, 5, 2, 20, 2, 5, 2, 95, 2, 5, 2, 20, 2, 5, 2, 470, 2, 5, 2, 20, 2, 5, 2, 95, 2, 5, 2, 20, 2, 5, 2, 470,

2, 5, 2, 20, 2, 5, 2, 95, 2, 5, 2, 20, 2, 5, 2, 95, 2, 5, 2, 20, 2, 5, 2, 20, 2, 5, 2, 5, 2, 2, 1.

At first a(2^(n+1)-1) = (3*5^n+5)/4 (n>=0). Let A be the sequence defined as follows:

A(0)=2; W(A(0))=5; A(1)=A(0),W(A(0))=2, 5; W(A(1))=2, 20.

More generally with A(n)=B(n), {3*5^n+5)/4; we define W(A(n))=B(n), (3*5^(n+1)+5)/4 and A(n+1)=A(n), W(A(n)).

Here we obtain A(1)=2, 5; W(A(1))=2, 20; A(2)=2, 5, 2, 20; W(A(2))=2, 5, 2, 95; A(3)=2, 5, 2, 20, 2, 5, 2, 95;

W(A(3))=2, 5, 2, 20, 2, 5, 2, 470; A(4)=2, 5, 2, 20, 2, 5, 2, 95, 2, 5, 2, 20, 2, 5, 2, 470, etc.

In fact: B(1)=2; B(2)=2, 5, 2; B(3)=2, 5, 2, 20, 2, 5, 2; B(4)=2, 5, 2, 20, 2, 5, 2, 95, 2, 5, 2, 20, 2, 5, 2, etc.

If we denote by <<A|UA|>> the subsequence of a between a(2^(n+1)-1) and a(2^(n+2)-1), the subsequence of a between a(2^(n+2)-1) and a(2^(n+3)-1) is given by <<A|A(n+1), A(n+1), UA|>>.

It seems that this sequence gives the numbers of 1 in the successive sets of 1 in the sequence A174835.

Links

Table of n, a(n) for n=0..92.

Example

a(1)=a(2^1-1)=(3*5^0+5)/4=2. a(3)=a(2^2-1)=(3*5+5)/4=5.
a(7)=a(2^3-1)=(75+5)/4=20. a(15)=a(2^4-1)=(3*125+5)/4=380/4=95.
Between 20 and 95 the subsequence of a is: 2, 5, 2, 5, 2, 2, 1.
Then with the definition, the subsequence of a, between 95 and 470 is:
A(2), A(2), 2, 5, 2, 5, 2, 2, 1, i.e., 2, 5, 2, 20, 2, 5, 2, 20, 2, 5, 2, 5, 2, 2, 1.

Crossrefs

Cf. A174835, A174837.

Sequence in context: A308698 A308569 A350073 * A110874 A010253 A065274

Adjacent sequences: A174975 A174976 A174977 * A174979 A174980 A174981

Keyword

easy,nonn,uned

Author

Richard Choulet, Apr 03 2010

Status

approved