A323612 Numbers k such that k^2 starts with at least the same number >= 2 of equal digits as does k itself.

88, 332, 334, 335, 336, 337, 338, 339, 664, 665, 667, 668, 669, 880, 881, 882, 883, 995, 996, 997, 998, 3317, 3318, 3319, 3320, 3321, 3322, 3323, 3324, 3325, 3326, 3327, 3328, 3329, 3332, 3334, 3335, 3336, 3337, 3338, 3339, 3340, 3341, 3342, 3343, 3344, 3345, 3346, 3347

Offset: 1

Author

Reiner Moewald, Jan 20 2019

Keywords

• nonn
• base

Examples

			332^2 = 110224, i.e., both the integer and its square start with two equal digits.
Also 334^2 = 111556, so 334 is a term.
		

Links

• Reiner Moewald, Table of n, a(n) for n = 1..24527

Programs

PARI

nbi(d) = my(nb=1); for(k=2, #d, if (d[k] == d[1], nb++, break)); nb;
isok(n) = my(nb = nbi(digits(n))); (nb > 1) && (nbi(digits(n^2)) >= nb); \\ Michel Marcus, Apr 24 2019

Python

def zahl(z):
   a = str(z)
   r = 0
   while r < len(a) and a[0] == a[r]:
      r = r + 1
   b = str(z*z)
   s = 0
   while r < len(b) and b[0] == b[s]:
      s = s + 1
   if r >= 2:
      return(s-r)
   else:
      return(-1)
anz = 0
for i in range(1000000):
   if zahl(i) >= 0:
      anz = anz +1
      print(anz, i)