cp's OEIS Frontend

A181866 a(1) = 1, a(2) = 2. For n >= 3, a(n) is found by concatenating the fourth powers of the first n-1 terms of the sequence and then dividing the resulting number by a(n-1).

%I A181866 #5 Mar 30 2012 18:40:13
%S A181866 1,2,58,200195112,580000000008023436288643185139644928
%N A181866 a(1) = 1, a(2) = 2. For n >= 3, a(n) is found by concatenating the fourth powers of the first n-1 terms of the sequence and then dividing the resulting number by a(n-1).
%C A181866 The calculations for the first few values of the sequence are
%C A181866 ... 2^4 = 16 so a(3) = 116/2 = 58
%C A181866 ... 58^4 = 11316496 so a(4) = 11611316496/58 = 200195112.
%C A181866 The value of a(6) is calculated in the Example section below.
%C A181866 For similarly defined sequences see A181754 through A181756 and
%C A181866 A181864 through A181870.
%F A181866 DEFINITION
%F A181866 a(1) = 1, a(2) = 2, and for n >= 3
%F A181866 (1)... a(n) = concatenate(a(1)^4,a(2)^4,...,a(n-1)^4)/a(n-1).
%F A181866 RECURRENCE RELATION
%F A181866 For n >= 2
%F A181866 (2)... a(n+2) = a(n+1)^3 + (100^F(n,4))*a(n)
%F A181866 = a(n+1)^3 + (10^F(3*n))*a(n),
%F A181866 where F(n,4) is the Fibonacci polynomial F(n,x) evaluated at x = 4
%F A181866 and where F(n) denotes the n-th Fibonacci number A000045(n).
%F A181866 F(n,4) = A001076(n).
%e A181866 The recurrence relation (2) above gives
%e A181866 a(6) = a(5)^3+10^144*a(4)
%e A181866 = 200 19511 20000 00000 00000 00000 00000 00000 00000 00195 11200
%e A181866 00080 97251 90261 07158 64917 75226 28886 69453 43420 83613 55167
%e A181866 37330 42401 44438 01550 47183 94579 01959 53586 66752.
%e A181866 a(6) has 153 digits.
%p A181866 #A181866
%p A181866 M:=5:
%p A181866 a:=array(1..M):s:=array(1..M):
%p A181866 a[1]:=1:a[2]:=2:
%p A181866 s[1]:=convert(a[1]^4,string):
%p A181866 s[2]:=cat(s[1],convert(a[2]^4,string)):
%p A181866 for n from 3 to M do
%p A181866 a[n] := parse(s[n-1])/a[n-1];
%p A181866 s[n]:= cat(s[n-1],convert(a[n]^4,string));
%p A181866 end do:
%p A181866 seq(a[n],n = 1..M);
%Y A181866 Cf. A000045, A001076 (F(n,4)), A181754, A181755, A181756, A181864, A181865,
%Y A181866 A181867, A181868, A181869, A181870
%K A181866 nonn,easy,base
%O A181866 1,2
%A A181866 _Peter Bala_, Nov 29 2010