OFFSET
1,1
COMMENTS
Absent numbers cannot appear in the sequence A135506. Moreover, if the first term of that sequence, which is 1, is replaced by any other positive integer, absent numbers still do not appear (see the link). The rest of the odd composite numbers are called present numbers, which are the sequence A262748.
LINKS
Serafín Ruiz-Cabello, On the use of the lowest common multiple to build a prime-generating recurrence, arXiv:1504.05041 [math.CO], 2015.
PROG
(Sage)
def triangle(q, m): # This is the first auxiliary program
if q >= m:
return False
Q = factor(q)
for par in Q:
if m % par[0] != 0:
return False
return True
def pairs(m): # This is the second auxiliary program
L = []
M = factor(m)
for par in M:
p = par[0]
for q in range(p-1, m, p):
if triangle(q, m):
L.append((p, q))
return L
def print_absents(n0, n): # This program gives a list with every absent number in the interval [n0, n]
L = []
m0 = n0+1-(n0%2)
for m in range(m0, n+1, 2):
if not is_prime(m):
if pairs(m) != []:
L.append(m)
return L
# Serafín Ruiz-Cabello, Sep 30 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Serafín Ruiz-Cabello, Sep 29 2015
STATUS
approved