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

Author

Michel Lagneau, Aug 12 2013

Keywords

• nonn
• base

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.

Examples

			169 and 196 are two successive squares.
		

Links

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

Crossrefs

Cf. A069567, A247305.

Programs

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 *)

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