OFFSET
1,1
COMMENTS
A triple exchange is a permutation of 3 elements in which all 3 three items change position. (For the triple "ABC", that would be "BCA" and "CAB".)
EXAMPLE
The first term is the prime 113, since 131 and 311 are also prime. Another term is 1013, since 1103 and 1301 are prime.
PROG
(Python)
from sympy import isprime
from itertools import combinations, permutations
def ok(n):
if n < 100 or not isprime(n): return False
s = list(str(n))
for i, j, k in combinations(range(len(s)), 3):
pset, w, x = {n}, s[:], s[:]
w[i], w[j], w[k] = w[j], w[k], w[i]
x[i], x[j], x[k] = x[k], x[i], x[j]
if w[0] != "0" and isprime(t:=int("".join(w))): pset.add(t)
if x[0] != "0" and isprime(t:=int("".join(x))): pset.add(t)
if len(pset) == 3: return True
return False
print([k for k in range(1920) if ok(k)]) # Michael S. Branicky, Sep 17 2024
CROSSREFS
KEYWORD
nonn,base
AUTHOR
James S. DeArmon, Sep 15 2024
EXTENSIONS
Terms corrected by Michael S. Branicky, Sep 17 2024
STATUS
approved