

A105822


For n > 2, a(n) > 0 not appeared previously is such that a(n1)^2+4*a(n2)*a(n) = d^2 is a minimal square, a(1)=1, a(2)=2.


14



1, 2, 3, 5, 8, 4, 12, 7, 10, 17, 6, 11, 21, 32, 13, 19, 14, 33, 20, 28, 24, 27, 42, 40, 18, 9, 35, 44, 39, 54, 48, 22, 15, 37, 52, 89, 30, 59, 23, 36, 99, 70, 16, 86, 47, 45, 92, 65, 157, 34, 123, 135, 222, 56, 136, 82, 29, 53, 102, 155, 25, 130, 87, 43, 170, 213, 63, 150, 57
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Is it a permutation of positive integers? Among first 2000 terms, first missing numbers are 233, 349, 394, 443, 449.
The sequence depends on seed terms a(1) and a(2); if a(1) = 1, a(3) = a(2)+1.


LINKS



MAPLE

N:= 1000: # to get a(1) to a(N)
S:= 'S':
a[1]:= 1: a[2]:= 2:
S[1]:= 1: S[2]:= 1:
for n from 3 to N do
ds:= map(t > rhs(op(t)), [msolve(x^2=a[n1]^2, 4*a[n2])]);
xmin:= infinity;
for d in ds do
found:= false;
for y from floor((a[n1]d)/(4*a[n2]))+1 do
xy:= 4*a[n2]*y + d;
cand:= (xy^2  a[n1]^2)/(4*a[n2]);
if cand >= xmin then found:= false; break fi;
if not assigned(S[cand]) then found:= true; break fi;
od:
if found then xmin:= cand; fi;
od:
a[n]:= xmin;
S[xmin]:= 1;
od:


MATHEMATICA

a = {1, 2}; Do[i = 1; While[MemberQ[a, i]  !IntegerQ[Sqrt[a[[1]]^2 + 4 a[[2]]*i]], i++]; AppendTo[a, i], {n, 3, 70}]; a (* Ivan Neretin, May 11 2015 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



