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A249896 a(n+1) is next smallest square not divisible by 10 beginning with a(n), initial term is 6.

%I A249896 #20 May 22 2025 10:21:41
%S A249896 6,64,64009,6400960036,640096003602877347904,
%T A249896 640096003602877347904912233550482787380625,
%U A249896 6400960036028773479049122335504827873806251020537411455326101704116338781035920283225
%N A249896 a(n+1) is next smallest square not divisible by 10 beginning with a(n), initial term is 6.
%C A249896 a(11) has 1374 digits, a(12) has 2749, a(13) has 5499, a(14) has 10998. - _Robert Israel_, Nov 25 2020
%H A249896 Robert Israel, <a href="/A249896/b249896.txt">Table of n, a(n) for n = 1..10</a>
%H A249896 Robert Israel, <a href="/A249896/a249896.txt">Table of n, a(n) for n = 1..14</a>
%p A249896 R:= 6: x:= 6: s:= 2:
%p A249896 for iter from 1 while length(x) < 1000 do
%p A249896   for d from 1 do
%p A249896    if d::even then sp:= 1+ 10^(d/2)*s
%p A249896    else
%p A249896      sp:= ceil(sqrt(10^d*x));
%p A249896      if sp mod 10 = 0 then sp:=sp+1; fi
%p A249896    fi;
%p A249896    if sp^2 < (x+1)*10^d then
%p A249896      x:= sp^2; s:= sp; R:= R, x; break
%p A249896    fi
%p A249896   od;
%p A249896 od:
%p A249896 R; # _Robert Israel_, Nov 25 2020
%o A249896 (PARI) a(n)=k=n; s=1; while(s<5*10^7, if(s%10, if(s^2\(10^(#Str(s^2)-#Str(k)))==k, print1(s^2, ", "); k=s^2)); s++)
%o A249896 a(7)
%o A249896 (Python)
%o A249896 def f(x):
%o A249896   print(x, end=', ')
%o A249896   n = x
%o A249896   s = 1
%o A249896   while s < 10**7:
%o A249896     if s % 10:
%o A249896       S = str(s**2)
%o A249896       if S.startswith(str(n)):
%o A249896         print(s**2, end=', ')
%o A249896         n = s**2
%o A249896     s += 1
%o A249896 f(7)
%Y A249896 Cf. A048559, A048561.
%K A249896 nonn,base
%O A249896 1,1
%A A249896 _Derek Orr_, Nov 08 2014