A249893 a(n+1) is next smallest square not divisible by 10 beginning with a(n), initial term is 2.

2, 25, 256, 256036, 2560361612769, 256036161276932002260000001, 256036161276932002260000001607597862784080913990785121

Offset: 1

Author

Derek Orr, Nov 08 2014

Keywords

• nonn
• base

Comments

a(12) has 1717 digits. - Michael S. Branicky, Feb 25 2021

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..11 (terms 1..10 from Hiroaki Yamanouchi)

Crossrefs

Cf. A048559, A048561.

Programs

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(2)

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(2)

Python

from math import isqrt
def anext(an):
  lo, hi = an*10, an*10 + 9
  while True:
    found = False
    if isqrt(hi)**2 > lo: return (isqrt(lo)+1)**2
    lo, hi = lo*10, hi*10 + 9
n, an = 1, 2
for n in range(2, 17):
  an = anext(an)
  print(n, an) # Michael S. Branicky, Feb 25 2021