A352329 Squares in A030299.

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

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
A352329_list = list(islice(A352329_gen(), 10)) # Chai Wah Wu, Mar 21-22 2022

Crossrefs

Cf. A030299, A240763.

Sequence in context: A250831 A184772 A015425 * A353025 A345609 A346283

Adjacent sequences: A352326 A352327 A352328 * A352330 A352331 A352332

Keyword

nonn,base

Author

Luca Onnis and Marco Ripà, Mar 12 2022

Status

approved