A174837 -id:A174837 - cp's OEIS frontend

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

Richard Choulet, Apr 03 2010

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

			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.

Cf. A174835, A174837.

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A174978 For definition see comments lines.

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