cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A346891 Positive numbers whose square starts with exactly 3 identical digits.

Original entry on oeis.org

149, 298, 334, 472, 667, 745, 882, 1054, 1055, 1056, 1057, 1058, 1490, 1491, 1492, 1493, 1825, 1826, 1827, 2108, 2109, 2356, 2581, 2788, 2789, 2980, 2981, 3161, 3162, 3332, 3333, 3335, 3336, 3337, 3338, 3339, 3340, 3341, 3342, 3343, 3344, 3345, 3346
Offset: 1

Views

Author

Bernard Schott, Aug 06 2021

Keywords

Comments

If m is a term 10*m is another term.
2357 is the first term of A131573 that is not in this sequence (see Example section), the next ones are 2582, 3334, ...

Examples

			149 is a term because 149^2 = 22201 starts with three 2's.
2357 is not a term because 2357^2 = 5555449 starts with four 5's.

Crossrefs

Subsequence of A131573.
Cf. A039685 (similar, with "ends"), A346812 (similar, with 2), A346892.

Programs

  • Mathematica
    Select[Range[32, 3350], (d = IntegerDigits[#^2])[[1]] == d[[2]] == d[[3]] != d[[4]] &] (* Amiram Eldar, Aug 06 2021 *)
  • Python
    def ok(n): s = str(n*n); return len(s) > 3 and s[0] == s[1] == s[2] != s[3]
print(list(filter(ok, range(3347)))) # Michael S. Branicky, Aug 06 2021

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

Original entry on oeis.org

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

Views

Author

Bernard Schott, Aug 08 2021

Keywords

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

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

A346940 Numbers whose square starts with exactly 4 identical digits.

Original entry on oeis.org

2357, 2582, 3334, 4714, 5774, 6667, 8165, 8819, 9428, 10542, 10543, 10544, 10545, 14907, 14908, 14909, 18257, 18258, 18259, 21081, 21082, 21083, 23570, 23571, 25819, 25820, 27888, 27889, 29813, 29814, 31622, 33332, 33333, 33335, 33336, 33337, 33338, 33339, 33340, 33341, 33342
Offset: 1

Views

Author

Bernard Schott, Aug 08 2021

Keywords

Comments

If m is a term, 10*m is another term.
Differs from A132391 where only at least 4 identical digits are required; indeed, 10541 is the first term of A132391 that is not in this sequence (see Example section), the next one is 33346.

Examples

			2357 is a term because 2357^2 = 5555449 starts with four 5's.
10541 is not a term because 10541^2 = 111112681 starts with five 1's.

Crossrefs

Cf. A346941, A346942.
Supersequences: A131573, A132391.
Similar with: A346812 (2 digits), A346891 (3 digits).

Programs

  • Mathematica
    q[n_] := SameQ @@ (d = IntegerDigits[n^2])[[1 ;; 4]] && d[[5]] != d[[1]]; Select[Range[100, 33350], 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]
print(list(filter(ok, range(33343)))) # Michael S. Branicky, Aug 08 2021
Showing 1-3 of 3 results.

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