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.

Previous Showing 101-109 of 109 results.

A119233 Numbers k such that the k-th triangular number contains only digits {6,7,9}.

Original entry on oeis.org

3, 11, 36, 36817576, 365512507857054543
Offset: 1

Views

Author

Giovanni Resta, May 10 2006

Keywords

Comments

Next term exceeds 4.4*10^17.

Links

Crossrefs

Cf. A000217, A119232. See A119034 for a table of cross-references.

Extensions

365512507857054543 from Max Alekseyev, Mar 10 2009

A119235 Numbers k such that the k-th triangular number contains only digits {6,8,9}.

Original entry on oeis.org

3, 11, 36, 371211, 421186108, 1180677745929588
Offset: 1

Views

Author

Giovanni Resta, May 10 2006

Keywords

Comments

Next term exceeds 4.4*10^18.

Links

Crossrefs

Cf. A000217, A119234. See A119034 for a table of cross-references.

Extensions

Lower bound updated by Max Alekseyev, Apr 30 2010

A119237 Numbers k such that the k-th triangular number contains only digits {7,8,9}.

Original entry on oeis.org

12, 132, 1332, 13332, 133332, 1247307, 1333332, 3949427, 13333332, 133333332, 1333333332, 13333333332, 133333333332, 397189873707, 1333333333332, 13333333333332, 133333333333332, 1333333333333332, 13333333333333332
Offset: 1

Views

Author

Giovanni Resta, May 10 2006

Keywords

Links

Crossrefs

Cf. A000217, A119236. See A119034 for a table of cross-references.

A218389 Numbers k such that the k-th triangular number contains only digits {0,2,4}.

Original entry on oeis.org

8944, 2209995667055, 6957333458215, 20001000974971249775
Offset: 1

Views

Author

Max Alekseyev, Oct 27 2012

Keywords

Comments

No other terms below 1.4*10^20.

Links

Crossrefs

Cf. A000217, A218390. See A119034 for a table of cross-references.

A218398 Numbers k such that the k-th triangular number contains only digits {0,2,7}.

Original entry on oeis.org

374184, 7385400, 203569507673559, 6663335616682084400
Offset: 1

Views

Author

Max Alekseyev, Oct 28 2012

Keywords

Comments

No other terms below 1.4*10^20.

Links

Crossrefs

Cf. A000217, A218397. See A119034 for a table of cross-references.

A218400 Numbers k such that the k-th triangular number contains only digits {0,4,7}.

Original entry on oeis.org

284, 3080, 97680, 9460126854061817544
Offset: 1

Views

Author

Max Alekseyev, Oct 28 2012

Keywords

Comments

No other terms below 1.4*10^20.

Links

Crossrefs

Cf. A000217, A218399. See A119034 for a table of cross-references.

A218402 Numbers k such that the k-th triangular number contains only digits {0,7,9}.

Original entry on oeis.org

44, 426096444, 12641976109035254775
Offset: 1

Views

Author

Max Alekseyev, Oct 28 2012

Keywords

Comments

No other terms below 1.4*10^20.

Links

Crossrefs

Cf. A000217, A218401. See A119034 for a table of cross-references.

A118706 Triangular numbers whose digits in base 12 are contained in {1,5,7,11}.

Original entry on oeis.org

1, 91, 1891, 3403, 403651, 4388203, 4468555, 41710411, 201553003, 213283531, 410970115, 428264011, 633021571, 642342403, 703181251, 4913725411, 28007409475, 41103462403, 90151709131, 90294438403, 337594212451, 443352832075, 1452321801451, 1483280069635, 4435473488491
Offset: 1

Views

Author

Walter Kehowski, May 24 2006

Keywords

Comments

In base 12 all primes greater than 3 end in a 1, 5, 7, or E, where X is 10 and E is eleven. In base 12 the sequence is 1, 77, 1117, 1E77, 175717, 1577577, 15E5E77, 11E75E77, 575EE577, 5E517E77, E5771E17, EE511E77, 157EE7E17, 15E151E17, 1775E1717, E5171E117, 551775E717, 7E71571E17, 1557E75EE77, 155EE511E17, 55517751117, 71E11E71E77. Note that all elements after the first either end in 17 or 77. In base 12 the n such that t=n(n+1)/2 end in the digits 1 or X, but not respectively.

Examples

			a(4) = 3403 = 1E77 in base 12.

Crossrefs

Cf. A000217, A118711, A119033, A119034.

Programs

  • Maple
    L:=[]: pd:={1,5,7,11}: for w to 1 do for n from 1 to 10^6 do t:=n*(n+1)/2; lod:=convert(t,base,12); sod:=convert(lod,set); if sod subset pd then L:=[op(L),[n,t]] fi; od od; L;
  • Mathematica
    Select[Accumulate[Range[822000]],SubsetQ[{1,5,7,11},IntegerDigits[ #,12]]&] (* Harvey P. Dale, Oct 18 2019 *)

Formula

a(n) = t if t is the n-th triangular number such that S subset {1,5,7,11}, where S is the set of digits of t in base 12.
a(n) = A000217(A118711(n)). - Amiram Eldar, Aug 02 2024

Extensions

a(22)-a(25) from Amiram Eldar, Aug 02 2024

A118711 Integers k such that the k-th triangular number t_k has all its base-12 digits contained in {1,5,7,11}.

Original entry on oeis.org

1, 13, 61, 82, 898, 2962, 2989, 9133, 20077, 20653, 28669, 29266, 35581, 35842, 37501, 99133, 236674, 286717, 424621, 424957, 821698, 941650, 1704301, 1722370, 2978413, 3328258, 4494466, 10022317, 40392829, 49870141, 50668882, 53933053
Offset: 1

Views

Author

Walter Kehowski, May 24 2006

Keywords

Comments

In base 12 all primes greater than 3 end in the digits 1, 5, 7, E, where X is 10 and E is 11. They are the digits that satisfy GCD(d,12)=1.
The sequence in base 12 is: 1, 11, 51, 6X, 62X, 186X, 1891, 5351, E751, EE51, 14711, 14E2X, 18711, 188XX, 19851, 49451, E4E6X, 119E11, 185891, 185E11, 33762X, 394E2X, 6X2351, 6E08XX, EE7751, 11460XX, 1608E6X, 3433E51, 1163E591, 14850051, 14E7632X, 1608E311, 18331451, 1870E191, 1974E311, ..., . Note that all elements end in 1 or X. The corresponding triangular numbers after the first end in the digits 17 or 77, but not respectively.

Examples

			82 = 6X_12 is a term since the triangular number t=82*(82+1)/2 = 3403 = 1E77_12.

Crossrefs

Cf. A000217, A118706, A119033, A119034.

Programs

  • Maple
    L:=[]: pd:={1,5,7,11}: for w to 1 do for n from 1 to 10^6 do t:=n*(n+1)/2; lod:=convert(t,base,12); sod:=convert(lod,set); if sod subset pd then L:=[op(L), [n,t]] fi; od od; L;
  • Mathematica
    fQ[n_] := Union@ Join[{1, 5, 7, 11}, IntegerDigits[n(n + 1)/2, 12]] == {1, 5, 7, 11}; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]], {n, 10^8}] (* Robert G. Wilson v *)

Formula

k is a term if the k-th triangular number t_k = k*(k+1)/2 has its base-12 digits contained in {1,5,7,11}.
A000217(a(n)) = A118706(n), or equivalently, a(n) = (sqrt(8*A118706(n)+1)-1)/2. - Amiram Eldar, Aug 02 2024

Extensions

Edited and extended (a(23)-a(32)) by Robert G. Wilson v, Jun 20 2006
Previous Showing 101-109 of 109 results.

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