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A352329 Squares in A030299. 3
1, 13527684, 34857216, 65318724, 73256481, 81432576, 139854276, 152843769, 157326849, 215384976, 245893761, 254817369, 326597184, 361874529, 375468129, 382945761, 385297641, 412739856, 523814769, 529874361, 537219684, 549386721, 587432169, 589324176, 597362481, 615387249 (list; graph; refs; listen; history; text; internal format)
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
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
A352329_list = list(islice(A352329_gen(), 10)) # Chai Wah Wu, Mar 21-22 2022
CROSSREFS
Sequence in context: A250831 A184772 A015425 * A353025 A345609 A346283
KEYWORD
nonn,base
AUTHOR
Luca Onnis and Marco Ripà, Mar 12 2022
STATUS
approved

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Last modified March 5 08:56 EST 2024. Contains 370538 sequences. (Running on oeis4.)