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.

A277946 Squares whose largest decimal digit is 2.

Original entry on oeis.org

121, 10201, 12100, 22201, 1002001, 1020100, 1022121, 1210000, 1212201, 2220100, 100020001, 100200100, 100220121, 102010000, 102212100, 121000000, 121022001, 121220100, 210221001, 222010000, 10000200001, 10002000100, 10002200121, 10020010000, 10020210201
Offset: 1

Views

Author

Colin Barker, Nov 05 2016

Keywords

Comments

A subsequence of A000290.
From Robert Israel, Nov 14 2016: (Start)
If n is a term, then so is 100*n.
The first term with an even number of digits is a(36) = 100021020121.
The first term with an even number of digits that is not of the form a(36)*100^k has at least 24 digits.
(End)

Links

Crossrefs

Cf. A000290, A277947, A277948, A277959.

Programs

  • Magma
    [n^2: n in [1..1000000] | Maximum(Intseq(n^2)) eq 2]; // Vincenzo Librandi, Nov 06 2016
  • Maple
    res:= NULL: B:= [1,2]:
for m from 1 to 10 do
  for q in B do
    for x from ceil(sqrt(10^m*q)) to floor(sqrt(10^m*q + 2/9*(10^m-1))) do
      if max(convert(x^2,base,10)) = 2 then res:= res, x^2 fi
  od od:
  for q in B do
     for x from ceil(sqrt(10^(m+1)*q)) to floor(sqrt(10^(m+1)*q + 2/9*(10^(m+1)-1))) do
       if max(convert(x^2,base,10)) = 2 then res:= res, x^2 fi
  od od:
  if m < 10 then B:= map(t -> (10*t,10*t+1,10*t+2),B) fi;
od:
res; # Robert Israel, Nov 14 2016
  • Mathematica
    fQ[n_] := Union[ IntegerDigits[ n^2]][[-1]] == 2; Select[ Range@100500, fQ]^2 (* Robert G. Wilson v, Nov 06 2016 *)
  • PARI
    L=List(); for(n=1, 10000, if(vecmax(digits(n^2))==2, listput(L, n^2))); Vec(L)
\\ See A277959 for more efficient code. - M. F. Hasler, Nov 16 2017

Formula

a(n) = A277959(n)^2. Intersection of A000290 and A277964. - M. F. Hasler, Nov 15 2017

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

A030175 When squared gives number composed of digits {1,2,3}.

Original entry on oeis.org

1, 11, 111, 36361, 363639, 461761, 3636361, 34815389, 362397739, 176412364139, 57637950363639, 3497458093147239, 56843832676142723489, 557963558954625926861
Offset: 1

Views

Author

Patrick De Geest

Keywords

Links

Crossrefs

Cf. A030174; A000290.
Cf. A006716 = A027675^2, A030176 = A030177^2, A058411^2 = A058412, ..., A058473^2 = A058474.
Cf. A136808, A136809, ..., A137147: n and n^2 have digits {...}.
Cf. A277959^2 = A277946 and A277960^2 = A277947: squares whose largest digit is 2 resp. 3.

Programs

  • Mathematica
    Do[ If[ Union[ Join[{1, 2, 3}, IntegerDigits[n^2] ] ] == {1, 2, 3}, Print[n] ], {n, 0, 10^9}]
  • PARI
    lista(nn) = for(n=1, nn, if(setminus(vecsort(digits(n^2), , 8), [1, 2, 3])==[], print1(n, ", "))) \\ Iain Fox, Nov 16 2017

Formula

a(n)^2 = A030174(n). - M. F. Hasler, Nov 16 2017

Extensions

More terms from Patrick De Geest, Mar 01 2000
More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 14 2005
Offset corrected by Iain Fox, Nov 16 2017

A277960 Numbers n such that 3 is the largest decimal digit of n^2.

Original entry on oeis.org

111, 351, 361, 1110, 1149, 1761, 3510, 3610, 10101, 10111, 10149, 11100, 11101, 11490, 17610, 35100, 36100, 36361, 36501, 45861, 100111, 100649, 101010, 101011, 101110, 101149, 101490, 110101, 111000, 111001, 111010, 114111, 114499, 114900, 176100, 176361
Offset: 1

Views

Author

Colin Barker, Nov 06 2016

Keywords

Links

Crossrefs

Cf. A277947, A277959, A277961.

Programs

  • PARI
    L=List(); for(n=1, 10000, if(vecmax(digits(n^2))==3, listput(L, n))); Vec(L)

A278936 Cubes whose largest decimal digit is 3.

Original entry on oeis.org

1331, 1030301, 1331000, 1003003001, 1030301000, 1331000000, 1000300030001, 1003003001000, 1030301000000, 1331000000000, 1000030000300001, 1000300030001000, 1003003001000000, 1030301000000000, 1331000000000000, 321302302131323213, 1000003000003000001
Offset: 1

Views

Author

Colin Barker, Dec 02 2016

Keywords

Examples

			321302302131323213 is in the sequence because 321302302131323213 = 684917^3 and its largest digit is 3.

Crossrefs

Cf. A000578, A277947 (same for squares), A278937 (the cube roots).

Programs

  • Magma
    [n^3: n in [1..2*10^7] | Max(Intseq(n^3)) eq 3]; // Bruno Berselli, Dec 02 2016
  • Mathematica
    Select[Range[1000010]^3,Max[IntegerDigits[#]]==3&] (* Harvey P. Dale, Feb 09 2019 *)
  • PARI
    select(n->vecmax(digits(n))==3, vector(1000000, n, n^3))

Formula

a(n) = A278937(n)^3.

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.

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.
Showing 1-7 of 7 results.

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