1,1

The corresponding sequence B is A389390.

A = 4176,B = 8793.

Multiset(4176) + Multiset(8793) = {1,4,6,7,3,7,8,9}.

Multiset(4176^2 = 17438976) = {1,7,4,3,8,9,7,6}.

Multiset(8793^2 = 77316849) = {7,7,3,1,6,8,4,9}.

All three multisets are {1,3,4,6,7,7,8,9}.

comp[n_] := If[Min[ DigitCount[n^2] - DigitCount[n]] < 0, {}, Block[{q, co, }, q = Sort@ IntegerDigits[n^2]; co = Join @@ (ConstantArray[First@ #, Max[ Last@#, 0]] & /@ (Tally[q] /. (Tally[ IntegerDigits@ n] /. {w_, h_Integer} :> {w, k_} -> {w, k-h}))); n + 0 Select[FromDigits /@ Permutations@ co, # >= n && Sort@ IntegerDigits[#^2] == q &]]]; Join @@ (comp /@ Range[74000]) (* Giovanni Resta, Oct 02 2025 *)

(Python)

from collections import Counter

from itertools import count, islice, permutations

from sympy.utilities.iterables import multiset_permutations

def AB_gen(): # generator of terms

for A in count(1):

msA, msA2, msB, bigger = Counter(str(A)), Counter(str(A**2)), [], True

if set(msA) - set(msA2): continue

for e in sorted(msA2):

if msA2[e] < msA[e]:

bigger = False

break

msB.extend([e]*(msA2[e]-msA[e]))

if not bigger or msB == []: continue

for mp in multiset_permutations(msB):

B = int("".join(map(str, mp)))

if B < A: continue

msB2 = Counter(str(B**2))

if msA2 == msB2:

yield A, B

print([A for A, B in islice(AB_gen(), 39)]) # Michael S. Branicky, Oct 02 2025

Cf. A389390.

Sequence in context: A168663 A043627 A250161 * A256836 A104918 A308752

Adjacent sequences: A389376 A389377 A389378 * A389380 A389381 A389382

nonn,base

Yuto Tsujino, Oct 02 2025

approved