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%I #34 Feb 18 2024 13:20:25
%S 169,24649,833569,20367169,214534609,368678401,372142681,392554969,
%T 407676481,771617284,1013021584,1212780625,1404075841,1567051396,
%U 1623848209,2538748996,2866103296,2898960964,3015437569,3967236196,4098688441,4937451289,5854239169
%N Smaller of two consecutive squares which are anagrams (permutations) of each other.
%C Given the n-th square, it is occasionally possible to form the (n+1)-th square using the same digits in a different order.
%C "Anagram" means that both squares must not only use the same digits but must use each digit the same number of times.
%H Michael S. Branicky, <a href="/A227692/b227692.txt">Table of n, a(n) for n = 1..10000</a>
%e 169 and 196 are two successive squares.
%p 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:
%t 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 *)
%o (Python)
%o from itertools import count, islice
%o def agen(): # generator of terms
%o ip, sp, hp = 0, 0, "0"
%o for i in count(1):
%o s = i*i
%o h = "".join(sorted(str(s)))
%o if h == hp: yield sp
%o ip, sp, hp = i, s, h
%o print(list(islice(agen(), 23))) # _Michael S. Branicky_, Feb 18 2024
%Y Cf. A069567, A247305.
%K nonn,base
%O 1,1
%A _Michel Lagneau_, Aug 12 2013
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