OFFSET
1,2
COMMENTS
Conjecture: there are infinitely many terms.
REFERENCES
John D. Dixon and Brian Mortimer, Permutation groups. Graduate Texts in Mathematics, 163. Springer-Verlag, New York, 1996. xii+346 pp. ISBN: 0-387-94599-7 MR1409812 (98m:20003).
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..3185
PROG
(Python)
from itertools import permutations
def pmap(s, m): return sum(s[i-1]*10**(m-i) for i in range(1, len(s)+1))
def agen():
m = 1
while True:
for s in permutations(range(1, m+1)): yield pmap(s, m)
m += 1
def aupton(terms):
alst, g = [], agen()
while len(alst) < terms: alst += [next(g)]
return alst
def is_perfect_square(n):
return round(n ** 0.5) ** 2 == n
print([x for x in aupton(5000000) if is_perfect_square(x)])
(Python)
from itertools import count, islice, permutations
from sympy import integer_nthroot
def A352329_gen(): # generator of terms
for l in count(1):
if (r := l*(l+1)//2 % 9) == 0 or r == 1 or r == 4 or r == 7:
m = tuple(10**(l-i-1) for i in range(l))
for p in permutations(range(1, l+1)):
if integer_nthroot(n := sum(prod(k) for k in zip(m, p)), 2)[1]:
yield n
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Luca Onnis and Marco Ripà, Mar 12 2022
STATUS
approved