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

1,1

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.

Links

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

Example

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).

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 *)

Prog

(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

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.

Sequence in context: A216056 A258544 A249529 * A132905 A100780 A104286

Adjacent sequences: A346939 A346940 A346941 * A346943 A346944 A346945

Keyword

nonn,base

Author

Bernard Schott, Aug 08 2021

Status

approved