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

6, 64, 64009, 6400960036, 640096003602877347904, 640096003602877347904912233550482787380625, 6400960036028773479049122335504827873806251020537411455326101704116338781035920283225

Offset: 1

Author

Derek Orr, Nov 08 2014

Keywords

• nonn
• base

Comments

a(11) has 1374 digits, a(12) has 2749, a(13) has 5499, a(14) has 10998. - Robert Israel, Nov 25 2020

Links

• Robert Israel, Table of n, a(n) for n = 1..10
• Robert Israel, Table of n, a(n) for n = 1..14

Crossrefs

Cf. A048559, A048561.

Programs

Maple

R:= 6: x:= 6: s:= 2:
for iter from 1 while length(x) < 1000 do
  for d from 1 do
   if d::even then sp:= 1+ 10^(d/2)*s
   else
     sp:= ceil(sqrt(10^d*x));
     if sp mod 10 = 0 then sp:=sp+1; fi
   fi;
   if sp^2 < (x+1)*10^d then
     x:= sp^2; s:= sp; R:= R, x; break
   fi
  od;
od:
R; # Robert Israel, Nov 25 2020

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++)
a(7)

Python

def f(x):
  print(x, end=', ')
  n = x
  s = 1
  while s < 10**7:
    if s % 10:
      S = str(s**2)
      if S.startswith(str(n)):
        print(s**2, end=', ')
        n = s**2
    s += 1
f(7)