Given value p, return last element of sequence < p - Fortran - while-loop

Question

I have a sequence of numbers as follows:
1 , 1, 5, 13, 41, 121, 365, ....
The first two values are:
N(1) = 1 and N(2) = 1
As from 3rd value, N(i) = 2*N(i-1) + 3*N(i-2)
The issue I am facing with is: If I give an argument of p, it should return me the last values of the sequence < p (Using fortran77).
For instance, if p = 90, it should return the value 41.

Answer 1

a = 1
b = 1
while b < p:
c = 2 * b + 3 * a
a = b
b = c
return a
The Fortran equivalent is:
function fct(p) result(a)
integer, intent(in) :: p
integer :: a, b, c
a = 1
b = 1
do while (b < p)
c = 2 * b + 3 * a
a = b
b = c
enddo
end function
program test
integer :: fct
external fct
print *,fct(90)
end program

Answer 2

Assuming you already have the sequence in a variable lst, and p set,
max(filter(lambda x:x<=p, lst))

Answer 3

def get_last_element(p):
n1 = 1
n2 = 1
while True:
if n2 > p:
return n1
n1, n2 = n2, 2*n2 + 3 * n1
print(get_last_element(90))

Answer 4

I wrote a piece of code in Fortran 2003. I defined a type which has memory for two last parts of the sequence.The procedure is a recursive function. The type can be used standalone to get n-th part of the sequence or efficiently placed in a loop to find parts in a row (not necessarily beginning at 1) as it has memory of previous parts. (compiler: gfortran 4.8).
The type is defined in mymod.f90 file as
module mymod
implicit none
type seq_t
integer :: saved_i = 0, saved_val_i = 0, saved_val_i_1 = 0
contains
procedure :: getpart => getpart_seq
end type
contains
recursive function getpart_seq(this,i) result(r)
class(seq_t) :: this
integer, intent(in) :: i
integer :: r,r_1,r_2
if (i.eq.1.or.i.eq.2) then
r = 1
elseif(i.eq.this%saved_i) then
r = this%saved_val_i
elseif(i.eq.this%saved_i-1) then
r = this%saved_val_i_1
else
r_1 = this%getpart(i-1)
r_2 = this%getpart(i-2)
r = 2*r_1 + 3*r_2
this%saved_val_i_1 = r_1
end if
this%saved_i = i
this%saved_val_i = r
end function getpart_seq
end module mymod
The main program for the requested case is
program main
use mymod
implicit none
type (seq_t) :: seq
integer :: i,p,tmp_new,tmp_old,ans
! Set the threshold here
p = 90
! loop over parts of the sequence
i = 0
do
i = i + 1
tmp_new = seq%getpart(i)
print*,tmp_new
if (tmp_new>p) then
ans = tmp_old
exit
end if
tmp_old = tmp_new
end do
print*,"The last part of sequence less then",p," is equal to",ans
end program
The outcome is
1
1
5
13
41
121
The last part of sequence less then 90 is equal to 41.