A227692 Smaller of two consecutive squares which are anagrams (permutations) of each other.

169, 24649, 833569, 20367169, 214534609, 368678401, 372142681, 392554969, 407676481, 771617284, 1013021584, 1212780625, 1404075841, 1567051396, 1623848209, 2538748996, 2866103296, 2898960964, 3015437569, 3967236196, 4098688441, 4937451289, 5854239169

Offset

1,1

Comments

Given the n-th square, it is occasionally possible to form the (n+1)-th square using the same digits in a different order.

"Anagram" means that both squares must not only use the same digits but must use each digit the same number of times.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

169 and 196 are two successive squares.

Maple

with(numtheory):for n from 1 to 80000 do:p1:=n^2:p2:= (n+1)^2:pp1:=convert(p1, base, 10): pp2:=convert(p2, base, 10):n1:=sort(pp1):n2:=sort(pp2): if n1=n2 then printf(`%d, `, p1):else fi:od:

Mathematica

lst = {}; k = 1; s = t = 0; ss = {0}; While[k < 155001, s = t; t += k; st = Sort@IntegerDigits@ t; If[ss == st, AppendTo[lst, s]]; ss = st; k += 2]; lst (* Robert G. Wilson v, Oct 24 2014 *)

Prog

(Python)
from itertools import count, islice
def agen(): # generator of terms
    ip, sp, hp = 0, 0, "0"
    for i in count(1):
        s = i*i
        h = "".join(sorted(str(s)))
        if h == hp: yield sp
        ip, sp, hp = i, s, h
print(list(islice(agen(), 23))) # Michael S. Branicky, Feb 18 2024

Crossrefs

Cf. A069567, A247305.

Sequence in context: A309907 A264222 A051477 * A260862 A006051 A069742

Adjacent sequences: A227689 A227690 A227691 * A227693 A227694 A227695

Keyword

nonn,base

Author

Michel Lagneau, Aug 12 2013

Status

approved