OFFSET
1,1
COMMENTS
Apparently 8 and the elements of A061743. - R. J. Mathar, Feb 19 2015
As x*y + x + y = (x + 1)*(y + 1) - 1 where x >= y > 1 we have k = a(n) is in the sequence if and only if k + 1 is an odd composite or k + 1 is an even number with more than 4 divisors. - David A. Corneth, Oct 15 2024
EXAMPLE
14 = 2*4 + 2 + 4.
15 = 3*3 + 3 + 3.
There is no way to express 16 in this form, so it is not in the sequence.
MATHEMATICA
sol[t_] := Solve[x >= y > 1 && x y + x + y == t, {x, y}, Integers];
Select[Range[200], sol[#] != {}&] (* Jean-François Alcover, Jul 28 2020 *)
PROG
(Python)
def aupto(limit):
cands = range(2, limit//3+1)
nums = [x*y+x+y for i, y in enumerate(cands) for x in cands[i:]]
return sorted(set(k for k in nums if k <= limit))
print(aupto(113)) # Michael S. Branicky, Aug 11 2021
(Python)
from sympy import primepi
def A254671(n):
def f(x): return int(n+(x>=7)+primepi(x+1)+primepi(x+1>>1))
m, k = n, f(n)
while m != k: m, k = k, f(k)
return m # Chai Wah Wu, Oct 14 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Alex Ratushnyak, Feb 04 2015
STATUS
approved