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.

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A295008 Numbers whose square has largest digit 8.

Original entry on oeis.org

9, 22, 28, 29, 41, 59, 62, 72, 78, 90, 91, 92, 94, 104, 109, 122, 126, 128, 135, 151, 159, 168, 169, 178, 184, 191, 192, 195, 196, 202, 209, 220, 221, 232, 241, 242, 259, 261, 262, 268, 278, 279, 280, 284, 285, 289, 290, 291, 292, 294, 295, 296, 298, 322, 328, 329, 341, 344, 349
Offset: 1

Views

Author

M. F. Hasler, Nov 12 2017

Keywords

Comments

Includes a*10^n+b for n >= 2 and [a,b] in {[4, 1], [9, 1], [2, 2], [9, 2], [1, 4], [6, 4], [9, 4], [8, 5], [4, 6], [9, 6], [5, 8], [8, 8], [9, 8], [1, 9], [2, 9], [4, 9], [6, 9], [8, 9], [9, 9]}. - Robert Israel, Nov 13 2017

Examples

			28 is in this sequence because 28^2 = 784 has 8 as largest digit.

Links

Crossrefs

Cf. A295018 (the corresponding squares), A277959 .. A277961 (same for digit 2 .. 4), A295005 .. A295009 (same for digit 5 .. 9).
Cf. A000290 (the squares).

Programs

  • Maple
    select(t -> max(convert(t^2,base,10))=8, [$1..1000]); # Robert Israel, Nov 13 2017
  • Mathematica
    Select[Range[400],Max[IntegerDigits[#^2]]==8&] (* Harvey P. Dale, Jun 02 2019 *)
  • PARI
    select( is_A295008(n)=n&&vecmax(digits(n^2))==8 , [0..999]) \\ The "n&&" avoids an error message for n=0.
  • Python
    def ok(n): return max(int(d) for d in str(n*n)) == 8
print(list(filter(ok, range(350)))) # Michael S. Branicky, Sep 22 2021

Formula

a(n) = sqrt(A295018(n)), where sqrt = A000196 or A000194 or A003059.

A136836 Numbers k such that k and k^2 use only the digits 0, 1, 2 and 9.

Original entry on oeis.org

0, 1, 10, 11, 100, 101, 110, 1000, 1001, 1010, 1011, 1100, 1101, 10000, 10001, 10010, 10011, 10100, 10110, 11000, 11001, 11010, 100000, 100001, 100010, 100011, 100100, 100101, 100110, 101000, 101001, 101100, 110000, 110001, 110010, 110100, 1000000, 1000001, 1000010, 1000011, 1000100
Offset: 1

Views

Author

Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008

Keywords

Comments

Generated with DrScheme.
Comparison of b-files indicates that the first difference from A136831 is at the 1262nd entry. - R. J. Mathar Apr 29 2008
More precisely, A278038(18) = 10101, A136827(294) = 10110001101 resp. A136808(1262) = A136831(1262) = 101100000000000 are the first terms from where on these four sequences differ from the present one; a(1262) = 101090009991101 is also the first term containing a digit > 1. - M. F. Hasler, Nov 15 2017

Examples

			101090009991101^2 = 10219190120000900002099192201.

Links

Crossrefs

Cf. A136808, A136809, A136810, ..., A137147 for other digit combinations.
See also A058412 = A058411^2: squares having only digits {0,1,2}, A277946 = A277959^2 = squares whose largest digit is 2.
The first 1261 terms are also a subsequence of A278038 (binary numbers without '111'), in turn a subsequence of the binary numbers A007088.

Programs

  • Mathematica
    With[{c={0,1,2,9}},Select[FromDigits/@Tuples[c,7],SubsetQ[c,IntegerDigits[#^2]]&]] (* Harvey P. Dale, Feb 11 2024 *)

A137146 Numbers k such that k and k^2 use only the digits 5, 6, 7 and 8.

Original entry on oeis.org

76, 766, 7666, 76666, 766666, 7666666, 76666666, 766666666, 7666666666, 76666666666, 766666666666, 7666666666666, 76666666666666, 766666666666666, 7666666666666666, 76666666666666666, 766666666666666666, 7666666666666666666, 76666666666666666666, 766666666666666666666
Offset: 1

Views

Author

Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008

Keywords

Comments

Generated with DrScheme.
The first digit of each term is either 7 or 8 and the last digit is 6. - Chai Wah Wu, May 25 2021

Examples

			766666666666666^2 = 587777777777776755555555555556.

Links

Crossrefs

Cf. A000290 (the squares); A136808, A136809, ..., A137147 for other digit combinations.
Cf. A058469 - A058472 and A058411, ..., A058474 for other digit combinations.
Cf. A277959, A277960, A277961, A295005, ..., A295009 (squares with largest digit = 2, 3, 4, 5, ..., 9).

Programs

  • Python
    from itertools import product
A137146_list = [n for n in (int(''.join(d)) for l in range(1,6) for d in product('5678',repeat=l)) if set(str(n**2)) <= set('5678')] # Chai Wah Wu, May 25 2021

Extensions

a(15)-a(20) from Pontus von Brömssen, Apr 12 2024

A295007 Numbers n such that the largest digit of n^2 is 7.

Original entry on oeis.org

24, 26, 42, 52, 61, 69, 74, 76, 82, 84, 85, 88, 124, 131, 132, 144, 154, 165, 166, 174, 181, 189, 194, 218, 224, 226, 234, 239, 240, 260, 265, 266, 269, 271, 274, 275, 276, 319, 326, 356, 371, 376, 384, 415, 416, 418, 419, 420, 421, 448, 455, 466, 474, 476, 520, 521, 524, 525, 526, 552
Offset: 1

Views

Author

M. F. Hasler, Nov 12 2017

Keywords

Examples

			24 is in this sequence because 24^2 = 576 has 7 as largest digit.

Links

Crossrefs

Cf. A295017 (the corresponding squares), A277959 .. A277961 (same for digit 2 .. 4), A295005 .. A295009 (same for digit 5 .. 9).
Cf. A000290 (the squares).

Programs

  • Maple
    filter:= proc(n) max(convert(n^2,base,10))=7 end proc:
select(filter, [$1..1000]); # Robert Israel, Feb 19 2019
  • PARI
    select( is_A295007(n)=n&&vecmax(digits(n^2))==7 , [0..999]) \\ The "n&&" avoids an error message for n=0.

Formula

a(n) = sqrt(A295017(n)), where sqrt = A000196 or A000194 or A003059.
Previous Showing 11-14 of 14 results.

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

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