OFFSET
0,1
COMMENTS
For n > 1, a(n) has digital root 3 or 4 depending on whether n is odd or even.
The 5-adic valuation of a(n)^2 + 1 is n+1. - William Hu, Dec 01 2023
REFERENCES
T. Koshy, "Intriguing Properties Of Three Related Number Sequences", in Journal of Recreational Mathematics, vol. 32(3) 210-3 2003-4 Baywood NY.
FORMULA
From Gerald McGarvey, Dec 12 2007: (Start)
For n > 0, a(n) = Sum_{k=0..n-1} a(k)^2 + n + 2.
Conjecture: a(n) is asymptotic to d - 1/2 -(5/2^3)/d -(65/2^7)/d^3 -(650/2^11)/d^5 -(19045/2^15)/d^7 -(274950/2^19)/d^9 -(6979050/2^23)/d^11 -(130292500/2^27)/d^13 ... where d = c^(2^n) and c is a constant = 1.288203192684485177845610784851700404829443712770079185959554466777577486352420255603915828361833141546.... (End)
MAPLE
a[0]:=2: for n from 1 to 8 do a[n]:=1+a[n-1]*(a[n-1]+1) od: seq(a[n], n=0..8); # Emeric Deutsch, Jun 13 2005
MATHEMATICA
NestList[1+#(#+1)&, 2, 10] (* Harvey P. Dale, Mar 30 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Lekraj Beedassy, Apr 11 2005
EXTENSIONS
More terms from Emeric Deutsch, Jun 13 2005
STATUS
approved