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 1-7 of 7 results.

A277948 Squares whose largest decimal digit is 4.

Original entry on oeis.org

4, 144, 324, 400, 441, 1024, 1444, 2304, 2401, 10404, 14400, 23104, 32041, 32400, 33124, 40000, 40401, 44100, 101124, 102400, 103041, 110224, 114244, 121104, 131044, 144400, 203401, 204304, 213444, 230400, 232324, 240100, 300304, 301401, 421201, 1004004
Offset: 1

Views

Author

Colin Barker, Nov 05 2016

Keywords

Comments

A subsequence of A158082, in turn a subsequence of A000290.

Links

Crossrefs

Cf. A000290 (the squares).
Cf. A277961 (square roots of these terms).
Cf. A277946, A277947, A295015, ..., A295019 (analog for largest digit = 2, 3, 5, ..., 9).
Cf. A058412, A058411, ..., A058474 and A136808, A136809, ..., A137147 for other restrictions on digits of squares.

Programs

  • Magma
    [n^2: n in [1..1000000] | Maximum(Intseq(n^2)) eq 4]; // Vincenzo Librandi, Nov 06 2016
  • Mathematica
    Select[Range[1100]^2,Max[IntegerDigits[#]]==4&] (* Harvey P. Dale, Jul 01 2017 *)
  • PARI
    L=List(); for(n=1, 10000, if(vecmax(digits(n^2))==4, listput(L, n^2))); Vec(L)

Formula

a(n) = A277961(n)^2. - M. F. Hasler, Nov 12 2017
Intersection of A000290 and A277966. - M. F. Hasler, Nov 15 2017

A295009 Numbers k such that the largest digit of k^2 is 9.

Original entry on oeis.org

3, 7, 13, 14, 17, 23, 27, 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, 103, 107, 113, 114, 117, 118, 123, 127, 130, 133, 134, 136, 137, 138, 139, 140, 141, 143, 147, 148, 153, 157, 158, 161, 163, 164, 167, 170, 171
Offset: 1

Views

Author

M. F. Hasler, Nov 12 2017

Keywords

Examples

			23 is in this sequence because 23^2 = 529 has 9 as largest digit.

Crossrefs

Cf. A295019 (the corresponding squares), A277959 .. A277961 (same for digit 2 .. 4), A295005 .. A295008 (same for digit 5 .. 8).
Cf. A000290 (the squares).

Programs

  • PARI
    select( is_A295009(n)=n&&vecmax(digits(n^2))==9 , [0..999]) \\ The "n&&" avoids an error message for n=0.

Formula

a(n) = sqrt(A295019(n)), where sqrt = A000196 or A000194 or A003059.

A295015 Squares whose largest digit is 5.

Original entry on oeis.org

25, 225, 1225, 1521, 2025, 2500, 3025, 4225, 5041, 11025, 12544, 13225, 21025, 22500, 24025, 34225, 35344, 42025, 44521, 52441, 55225, 112225, 122500, 133225, 135424, 150544, 151321, 152100, 202500, 212521, 235225, 245025, 250000, 251001, 252004, 255025, 302500
Offset: 1

Views

Author

M. F. Hasler, Nov 12 2017

Keywords

Links

Crossrefs

Cf. A295015 (square roots of the terms); A277946, A277947, A277948, A295016 .. A295019 (analog for digits 2 through 9); A295025 (analog for cubes).
Cf. A000290 (the squares).

Programs

  • Mathematica
    Select[Range[600]^2,Max[IntegerDigits[#]]==5&] (* Harvey P. Dale, Aug 19 2022 *)
  • PARI
    is_A295015(n)=issquare(n)&&n&&vecmax(digits(n))==5 \\ The "n&&" avoids an error message for n = 0.
  • Python
    from math import isqrt
def aupto(limit):
  alst, rootlimit = [], isqrt(limit)
  for k in range(1, rootlimit+1):
    if max(str(k*k)) == "5": alst.append(k*k)
  return alst
print(aupto(302500)) # Michael S. Branicky, May 15 2021

Formula

a(n) = A295005(n)^2.

A295024 Cubes whose largest digit is 9.

Original entry on oeis.org

729, 2197, 4096, 4913, 6859, 9261, 19683, 21952, 24389, 29791, 35937, 39304, 59319, 68921, 79507, 91125, 97336, 110592, 117649, 185193, 195112, 205379, 226981, 287496, 328509, 357911, 389017, 438976, 493039, 592704, 704969, 729000, 912673, 941192, 970299, 1092727, 1191016
Offset: 1

Views

Author

M. F. Hasler, Nov 13 2017

Keywords

Comments

For any term a(n), all numbers of the form a(n)*10^3k, k >= 0, are in this sequence. We could call "primitive" the terms not of this form, i.e., those without trailing '0'.

Examples

			2197 is in the sequence because it is a cube, 2197 = 13^3, and its largest digit is 9.

Crossrefs

Cf. A294999 (the corresponding cube roots), A278936, A294663, A295025, A295021, A295022, A295023 (same for digit 3 .. 8), A295019 (same for squares).
Cf. A000578 (the cubes).

Programs

  • PARI
    for(n=1,150, vecmax(digits(n^3))==8 &&print1(n^3,","))

Formula

a(n) = A294999(n)^3.

A295016 Squares whose largest digit is 6.

Original entry on oeis.org

16, 36, 64, 256, 361, 625, 1156, 1600, 2116, 2601, 3136, 3364, 3600, 4356, 4624, 5625, 6241, 6400, 6561, 11236, 11664, 13456, 14161, 14641, 15625, 16641, 20164, 21316, 24336, 25600, 26244, 30625, 36100, 41616, 42436, 43264, 46225, 46656, 50625, 53361, 56644, 60025, 60516, 61504
Offset: 1

Views

Author

M. F. Hasler, Nov 12 2017

Keywords

Links

Crossrefs

Cf. A295006 (square roots of the terms); A277946, A277947, A277948, A295015 .. A295019 (analog for digits 2 through 9), A295021 (analog for cubes).
Cf. A000290 (the squares).

Programs

  • Mathematica
    Select[Range[250]^2,Max[IntegerDigits[#]]==6&] (* Harvey P. Dale, Jun 14 2025 *)
  • PARI
    is_A295016(n)=issquare(n)&&n&&vecmax(digits(n))==6 \\ The "n&&" avoids an error message for n = 0.

Formula

a(n) = A295006(n)^2.

A295018 Squares whose largest digit is 8.

Original entry on oeis.org

81, 484, 784, 841, 1681, 3481, 3844, 5184, 6084, 8100, 8281, 8464, 8836, 10816, 11881, 14884, 15876, 16384, 18225, 22801, 25281, 28224, 28561, 31684, 33856, 36481, 36864, 38025, 38416, 40804, 43681, 48400, 48841, 53824, 58081, 58564, 67081, 68121, 68644, 71824, 77284, 77841, 78400
Offset: 1

Views

Author

M. F. Hasler, Nov 12 2017

Keywords

Links

Crossrefs

Cf. A295008 (square roots of the terms), A277946 - A277948 (same for digit 2..4), A295015 - A295019 (same for digit 5..9).
Cf. A000290 (the squares).

Programs

  • Maple
    Res:= NULL: count:= 0:
for n from 1 while count < 50 do
  if max(convert(n^2,base,10))=8 then
    count:= count+1; Res:= Res, n^2;
  fi
od:
Res; # Robert Israel, Jul 21 2019
  • Mathematica
    Select[Range[300]^2,Max[IntegerDigits[#]]==8&] (* Harvey P. Dale, Jul 08 2020 *)
  • PARI
    is_A295018(n)=issquare(n)&&n&&vecmax(digits(n))==8 \\ "&&n" avoids an error message for n=0.

Formula

a(n) = A295008(n)^2.

A295017 Squares whose largest digit is 7.

Original entry on oeis.org

576, 676, 1764, 2704, 3721, 4761, 5476, 5776, 6724, 7056, 7225, 7744, 15376, 17161, 17424, 20736, 23716, 27225, 27556, 30276, 32761, 35721, 37636, 47524, 50176, 51076, 54756, 57121, 57600, 67600, 70225, 70756, 72361, 73441, 75076, 75625, 76176, 101761, 106276, 126736, 137641, 141376
Offset: 1

Views

Author

M. F. Hasler, Nov 12 2017

Keywords

Links

Crossrefs

Cf. A295007 (square roots of the terms), A277946 .. A277948 (same for digit 2 .. 4), A295015 .. A295019 (same for digit 5 .. 9), A295022 (same for cubes).
Cf. A000290 (the squares).

Programs

  • Mathematica
    Select[Range[1000]^2,Max[IntegerDigits[#]]==7&] (* Harvey P. Dale, Dec 15 2024 *)
  • PARI
    is_A295017(n)=issquare(n)&&n&&vecmax(digits(n))==7 \\ The "n&&" avoids an error message for n=0.

Formula

a(n) = A295007(n)^2.
Showing 1-7 of 7 results.

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

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