OFFSET
1,1
COMMENTS
Similar to Bolyai expansion. Uses the fact that for 0<p<1, 2<(2+p)^2-2<7.
LINKS
Yuriy Sibirmovsky, Table of n, a(n) for n = 1..250
Eric Weisstein's World of Mathematics, Bolyai Expansion.
EXAMPLE
Pi^2=7+2+p1, thus a(1)=7;
(2+p1)^2=6+2+p2, thus a(2)=6;
(2+p2)^2=2+2+p3, thus a(3)=2; ... 0<pn<1.
MATHEMATICA
Nm=100;
A=Table[1, {j, 1, Nm}];
V=Table[1, {j, 1, Nm}];
P=Pi;
p0=P;
Do[p1=Floor[p0^2]-2;
A[[j]]=p1;
p0=N[2+p0^2-Floor[p0^2], 300], {j, 1, Nm}];
Do[v0=Sqrt[A[[n]]];
Do[v1=A[[n-j]]+v0;
v0=Sqrt[v1], {j, 1, n-1}];
V[[n]]=v0, {n, 1, Nm}];
A
CROSSREFS
KEYWORD
nonn
AUTHOR
Yuriy Sibirmovsky, Sep 03 2016
STATUS
approved