A346942 Numbers whose square starts and ends with exactly 4 identical digits.

235700, 258200, 333400, 471400, 577400, 666700, 816500, 881900, 942800, 1054200, 1054300, 1054400, 1054500, 1490700, 1490800, 1490900, 1825700, 1825800, 1825900, 2108100, 2108200, 2108300, 2357100, 2581900, 2788800, 2788900, 2981300, 2981400, 3162200, 3333200, 3333300

Offset: 1

Author

Bernard Schott, Aug 08 2021

Keywords

• nonn
• base

Comments

Terms are equal to 100 times the primitive terms of A346940, those that have no trailing zero in decimal representation, hence all terms end with exactly 00.

Examples

			258200 is a term because 258200^2 = 66667240000 starts with four 6's and ends with four 0's.
3334700 is not a term because 3334700^2 = 1111155560000 starts with five 1's (and ends with four 0's).
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Numbers whose square '....' with exactly k identical digits:

---------------------------------------------------------------------------

| k \'....'| starts | ends | starts and ends |

---------------------------------------------------------------------------

| k = 2 | A346812 | A346678 | A346774 |

| k = 3 | A346891 | A039685 | A346892 |

| k = 4 | A346940 | 100*A067251 | this sequence |

---------------------------------------------------------------------------

Cf. A346926.

Programs

Mathematica

q[n_] := SameQ @@ (d = IntegerDigits[n^2])[[1 ;; 4]] && d[[5]] != d[[1]] && SameQ @@ d[[-4 ;; -1]] && d[[-5]] != d[[-1]]; Select[Range[10000, 3333300], q] (* Amiram Eldar, Aug 08 2021 *)

Python

def ok(n):
  s = str(n*n)
  return len(s) > 4 and s[0] == s[1] == s[2] == s[3] != s[4] and s[-1] == s[-2] == s[-3] == s[-4] != s[-5]
print(list(filter(ok, range(3333333)))) # Michael S. Branicky, Aug 08 2021

Python

A346942_list = [100*n for n in range(99,10**6) if n % 10 and (lambda x:x[0]==x[1]==x[2]==x[3]!=x[4])(str(n**2))] # Chai Wah Wu, Oct 02 2021