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A346942
Numbers whose square starts and ends with exactly 4 identical digits.
3
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.
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
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Aug 08 2021
STATUS
approved