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 1-8 of 8 results.

A225218 Square numbers containing all the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

Original entry on oeis.org

1026753849, 1042385796, 1098524736, 1237069584, 1248703569, 1278563049, 1285437609, 1382054976, 1436789025, 1503267984, 1532487609, 1547320896, 1643897025, 1827049536, 1927385604, 1937408256, 2076351489, 2081549376, 2170348569, 2386517904, 2431870596
Offset: 1

Views

Author

Reiner Moewald, May 02 2013

Keywords

Comments

The first term having a repeated digit is 10057482369. - Colin Barker, Jan 15 2014

Examples

			1026753849 is in the sequence because 1026753849 = 32043^2 and 1026753849 contains all ten digits 0, ..., 9.

Links

Crossrefs

Supersequence of A036745.
Cf. A235717-A235724.

Programs

  • Mathematica
    Select[#^2 &[Range[1000000]], Length[Union[IntegerDigits[#]]] == 10 &] (* Geoffrey Critzer, Jan 04 2015 *)
  • PARI
    s=[]; for(n=1, 100000, if(#vecsort(eval(Vec(Str(n^2))), , 8)==10, s=concat(s, n^2))); s \\ Colin Barker, Jan 15 2014
  • Python
    from itertools import count, islice
def c(n): return len(set(str(n))) == 10
def agen(): yield from (k*k for k in count(31622) if c(k*k))
print(list(islice(agen(), 21))) # Michael S. Branicky, Dec 27 2022

Formula

a(n) = A054038(n)^2. - Colin Barker, Jan 15 2014

A235717 Squares which have one or more occurrences of exactly two different digits.

Original entry on oeis.org

16, 25, 36, 49, 64, 81, 100, 121, 144, 225, 400, 441, 484, 676, 900, 1444, 7744, 10000, 11881, 29929, 40000, 44944, 55225, 69696, 90000, 1000000, 4000000, 9000000, 9696996, 100000000, 400000000, 900000000, 6661661161, 10000000000, 40000000000, 90000000000
Offset: 1

Views

Author

Colin Barker, Jan 15 2014

Keywords

Comments

The first term having a repeated digit is 100.
This sequence is the same as A018885, except that A018885 has four additional leading terms.

Examples

			69696 is in the sequence because 69696 = 264^2 and 69696 contains exactly two different digits: 6 and 9.

Crossrefs

Cf. A235718-A235724, A225218.

Programs

  • PARI
    s=[]; for(n=1,10000, if(#vecsort(eval(Vec(Str(n^2))),,8)==2, s=concat(s, n^2))); s

Formula

a(n) = A016069(n)^2.

A235718 Squares which have one or more occurrences of exactly three different digits.

Original entry on oeis.org

169, 196, 256, 289, 324, 361, 529, 576, 625, 729, 784, 841, 961, 1156, 1225, 1521, 1600, 1681, 2025, 2116, 2209, 2500, 3136, 3364, 3600, 3844, 3969, 4225, 4489, 4624, 4900, 5625, 5776, 5929, 6400, 6561, 6889, 7225, 8100, 8281, 8464, 8836, 9409, 10201, 10404
Offset: 1

Views

Author

Colin Barker, Jan 15 2014

Keywords

Comments

The first term having a repeated digit is 1156.

Examples

			5929 is in the sequence because 5929 = 77^2 and 5929 contains exactly three different digits: 2, 5 and 9.

Links

Crossrefs

Cf. A054031, A225218, A235717, A235719-A235724.

Programs

  • PARI
    s=[]; for(n=1, 200, if(#vecsort(eval(Vec(Str(n^2))),,8)==3, s=concat(s, n^2))); s

Formula

a(n) = A054031(n)^2.

A235723 Squares which have one or more occurrences of exactly eight different digits.

Original entry on oeis.org

10278436, 10673289, 10679824, 10837264, 13498276, 13527684, 13675204, 13860729, 13942756, 16378209, 16785409, 17280649, 17430625, 19847025, 20584369, 20738916, 21307456, 21473956, 21743569, 23078416, 23174596, 23970816, 24137569, 24671089, 24870169, 28901376
Offset: 1

Views

Author

Colin Barker, Jan 15 2014

Keywords

Comments

The first term having a repeated digit is 101465329.

Examples

			10278436 is in the sequence because 10278436 = 3206^2 and 10278436 contains exactly eight different digits: 0, 1, 2, 3, 4, 6, 7 and 8.

Links

Crossrefs

Cf. A235717-A235722, A235724, A225218.

Programs

  • PARI
    s=[]; for(n=1, 10000, if(#vecsort(eval(Vec(Str(n^2))),,8)==8, s=concat(s, n^2))); s

Formula

a(n) = A054036(n)^2.

A235719 Squares which have one or more occurrences of exactly four different digits.

Original entry on oeis.org

1024, 1089, 1296, 1369, 1764, 1849, 1936, 2304, 2401, 2601, 2704, 2809, 2916, 3025, 3249, 3481, 3721, 4096, 4356, 4761, 5041, 5184, 5329, 5476, 6084, 6241, 6724, 7056, 7396, 7569, 7921, 8649, 9025, 9216, 9604, 9801, 10609, 10816, 11025, 11236, 12544, 12996
Offset: 1

Views

Author

Colin Barker, Jan 15 2014

Keywords

Comments

The first term having a repeated digit is 10609.

Examples

			5329 is in the sequence because 5329 = 73^2 and 5329 contains exactly four different digits: 2, 3, 5 and 9.

Links

Crossrefs

Cf. A235717, A235718, A235720-A235724, A225218.

Programs

  • Mathematica
    Select[Range[150]^2,Length[Union[IntegerDigits[#]]]==4&] (* Harvey P. Dale, May 03 2018 *)
  • PARI
    s=[]; for(n=1, 300, if(#vecsort(eval(Vec(Str(n^2))),,8)==4, s=concat(s, n^2))); s

Formula

a(n) = A054032(n)^2.

A235720 Squares which have one or more occurrences of exactly five different digits.

Original entry on oeis.org

12769, 13456, 13689, 13924, 15376, 15876, 16384, 17689, 17956, 18496, 18769, 20164, 20736, 21609, 21904, 23104, 23409, 23716, 28561, 29584, 30276, 30625, 30976, 31684, 32041, 32761, 34596, 35721, 36481, 37249, 38025, 38416, 39204, 39601, 41209, 43681, 45369
Offset: 1

Views

Author

Colin Barker, Jan 15 2014

Keywords

Comments

The first term having a repeated digit is 100489.

Examples

			30976 is in the sequence because 30976 = 176^2 and 30976 contains exactly five different digits: 0, 3, 6, 7 and 9.

Links

Crossrefs

Cf. A235717-A235719, A235721-A235724, A225218.

Programs

  • PARI
    s=[]; for(n=1, 1200, if(#vecsort(eval(Vec(Str(n^2))),,8)==5, s=concat(s, n^2))); s

Formula

a(n) = A054033(n)^2.

A235721 Squares which have one or more occurrences of exactly six different digits.

Original entry on oeis.org

103684, 104329, 104976, 107584, 123904, 124609, 132496, 134689, 139876, 140625, 157609, 162409, 164025, 170569, 173056, 180625, 195364, 198025, 207936, 209764, 214369, 237169, 254016, 257049, 258064, 259081, 279841, 293764, 310249, 318096, 321489, 326041
Offset: 1

Views

Author

Colin Barker, Jan 15 2014

Keywords

Comments

The first term having a repeated digit is 1028196.

Examples

			124609 is in the sequence because 124609 = 353^2 and 124609 contains exactly six different digits: 0, 1, 2, 4, 6 and 9.

Links

Crossrefs

Cf. A235717-A235720, A235722-A235724, A225218.

Programs

  • PARI
    s=[]; for(n=1, 1200, if(#vecsort(eval(Vec(Str(n^2))),,8)==6, s=concat(s, n^2))); s

Formula

a(n) = A054034(n)^2.

A235722 Squares which have one or more occurrences of exactly seven different digits.

Original entry on oeis.org

1034289, 1046529, 1048576, 1054729, 1056784, 1073296, 1075369, 1085764, 1238769, 1247689, 1354896, 1380625, 1382976, 1432809, 1507984, 1605289, 1607824, 1630729, 1695204, 1708249, 1750329, 1763584, 1803649, 1827904, 1836025, 1890625, 1946025, 1974025
Offset: 1

Views

Author

Colin Barker, Jan 15 2014

Keywords

Comments

The first term having a repeated digit is 10137856.

Examples

			1247689 is in the sequence because 1247689 = 1117^2 and 1247689 contains exactly seven different digits: 1, 2, 4, 6, 7, 8 and 9.

Links

Crossrefs

Cf. A235717-A235721, A235723, A235724, A225218.

Programs

Formula

a(n) = A054035(n)^2.
Showing 1-8 of 8 results.

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