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 1-4 of 4 results.

A360803 Numbers whose squares have a digit average of 8 or more.

Original entry on oeis.org

3, 313, 94863, 298327, 987917, 3162083, 9893887, 29983327, 99477133, 99483667, 197483417, 282753937, 314623583, 315432874, 706399164, 773303937, 894303633, 947047833, 948675387, 989938887, 994927133, 994987437, 998398167, 2428989417, 2754991833, 2983284917, 2999833327
Offset: 1

Views

Author

Dmitry Kamenetsky, Feb 21 2023

Keywords

Comments

This sequence is infinite. For example, numbers floor(30*100^k - (5/3)*10^k) beginning with 2 followed by k 9s, followed by 8 and k 3s, have a square whose digit average converges to (but never equals) 8.25. [Corrected and formula added by M. F. Hasler, Apr 11 2023]
Only a few examples are known whose square has a digit average of 8.25 and above: 3^2 = 9, 707106074079263583^2 = 499998999999788997978888999589997889 (digit average 8.25), 94180040294109027313^2 = 8869879989799999999898984986998979999969 (digit average 8.275).
This is the union of A164772 (digit average = 8) and A164841 (digit average > 8). - M. F. Hasler, Apr 11 2023

Examples

			94863 is in the sequence, because 94863^2 = 8998988769, which has a digit average of 8.1 >= 8.

Links

Crossrefs

Cf. A004159, A185679.
Cf. A164772 (digit average = 8), A164841 (digit average > 8).

Programs

  • PARI
    isok(k) = my(d=digits(k^2)); vecsum(d)/#d >= 8; \\ Michel Marcus, Feb 22 2023
  • Python
    def ok(n): d = list(map(int, str(n**2))); return sum(d) >= 8*len(d)
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Feb 22 2023

A378925 Positive numbers whose squares have at most one digit less than 8.

Original entry on oeis.org

1, 2, 3, 7, 9, 17, 83, 2983, 298327
Offset: 1

Views

Author

Zhining Yang, Dec 11 2024

Keywords

Comments

No terms > 298327 with less than 11 digits.
No terms > 298327 with less than 22 digits. - Michael S. Branicky, Dec 11 2024

Examples

			298327 is a term because 298327^2 = 88998998929 has only one digit that is less than 8.

Crossrefs

Cf. A053934, A360822, A378926, A378927.

Programs

  • Mathematica
    Select[Range[10^6], Count[IntegerDigits[#^2], _?(#1 < 8 &)] < 2 &]

A378926 Positive numbers whose squares have at most two digits less than 9.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 17, 23, 27, 30, 31, 63, 77, 97, 173, 313
Offset: 1

Views

Author

Zhining Yang, Dec 11 2024

Keywords

Comments

No terms > 313 with less than 16 digits.
No terms > 313 with less than 1040 digits. - Michael S. Branicky, Dec 11 2024

Examples

			313 is a term because 313^2 = 97969 has only two digits that are less than 9.

Crossrefs

Cf. A053934, A360822, A378925, A378927.

Programs

  • Mathematica
    Select[Range[10^6], Count[IntegerDigits[#^2], _?(#1 < 9 &)] < 3&]

A378927 Positive numbers whose squares have at most three digits less than 9.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 36, 37, 43, 44, 47, 53, 54, 57, 63, 64, 67, 70, 73, 77, 83, 86, 87, 89, 93, 95, 96, 97, 98, 99, 114, 173, 187, 223, 243, 263, 264, 303, 307, 313, 314, 315, 316, 437, 447, 547, 707, 964, 997, 1414, 2236, 2827, 3033, 3114, 3148, 3161
Offset: 1

Views

Author

Zhining Yang, Dec 11 2024

Keywords

Comments

No terms > 3161 with less than 16 digits.
No terms > 3161 with less than 101 digits. - Michael S. Branicky, Dec 11 2024

Examples

			3161 is a term because 3161^2 = 9991921 has only three digits that are less than 9.

Crossrefs

Cf. A053934, A360822, A378925, A378926.

Programs

  • Mathematica
    Select[Range[10^6], Count[IntegerDigits[#^2], _?(#1 < 9 &)] < 4 &]
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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