A181864 a(1) = 1, a(2) = 2. For n >= 3, a(n) is found by concatenating the squares of the first n-1 terms of the sequence and then dividing the resulting number by a(n-1).

1, 2, 7, 207, 700207, 207000000700207, 70020700000000000000207000000700207, 2070000007002070000000000000000000000000000000000070020700000000000000207000000700207

Offset: 1

Author

Peter Bala, Nov 28 2010

Keywords

• nonn
• easy

Comments

The calculations for the first few values of the sequence are

... 2^2 = 4 so a(3) = 14/2 = 7

... 7^2 = 49 so a(4) = 1449/7 = 207

... 207^2 = 42849 so a(5) = 144942849/207 = 700207.

For similarly defined sequences see A181754 through A181756 and A181865 through

A181870.

Crossrefs

A000129, A113225, A181754, A181755, A181756, A181865, A181866,A181867, A181868, A181869, A181870

Programs

Maple

#A181864
M:=8: a:=array(1..M):s:=array(1..M):
a[1]:=1:a[2]:=2:
s[1]:=convert(a[1]^2,string):
s[2]:=cat(s[1],convert(a[2]^2,string)):
for n from 3 to M do
a[n] := parse(s[n-1])/a[n-1];
s[n]:= cat(s[n-1],convert(a[n]^2,string));
end do:
seq(a[n],n = 1..M);

Formula

DEFINITION

a(1) = 1, a(2) = 2, and for n >= 3

(1)... a(n) = concatenate(a(1)^2,a(2)^2,...,a(n-1)^2)/a(n-1).

RECURRENCE RELATION

For n >= 2

(2)...a(n+2) = a(n+1) + 10^F(n,2)*a(n) = a(n+1) + 10^Pell(n)*a(n),

where F(n,2) is the Fibonacci polynomial F(n,x) evaluated at x = 2

and where Pell(n) = A000129(n).

RELATION WITH OTHER SEQUENCES

a(n) has A113225(n-2) digits.

a(n)^2 has Pell(n-1) digits.