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 1-6 of 6 results.

A037393 Numbers k such that every base-5 digit of k is a base-6 digit of k.

Original entry on oeis.org

1, 2, 3, 4, 6, 12, 18, 24, 31, 46, 56, 62, 75, 81, 87, 90, 91, 92, 93, 94, 99, 118, 124, 145, 150, 157, 226, 232, 243, 245, 291, 300, 306, 307, 308, 311, 312, 314, 322, 326, 332, 336, 337, 338, 341, 362, 372, 374, 378, 411, 416, 418
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A007091, A007092.
Cf. A037394, A037395, A037396, A037397.

Programs

  • Haskell
    import Data.List ((\\), nub)
a037393 n = a037393_list !! (n-1)
a037393_list = filter f [1..] where
   f x = null $ nub (ds 5 x) \\ nub (ds 6 x)
   ds b x = if x > 0 then d : ds b x' else []  where (x', d) = divMod x b
-- Reinhard Zumkeller, May 30 2013

A037394 Numbers k such that every base-5 digit of k is a base-7 digit of k.

Original entry on oeis.org

1, 2, 3, 4, 17, 51, 66, 102, 109, 123, 156, 158, 162, 206, 218, 312, 317, 324, 361, 381, 416, 418, 423, 458, 462, 463, 466, 467, 468, 472, 494, 518, 545, 546, 549, 556, 557, 559, 562, 584, 606, 619, 621, 630, 640, 651, 658, 687
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A007091, A007093.
Cf. A037393, A037395, A037396, A037397.

Programs

  • Haskell
    import Data.List ((\\), nub)
a037394 n = a037394_list !! (n-1)
a037394_list = filter f [1..] where
   f x = null $ nub (ds 5 x) \\ nub (ds 7 x)
   ds b x = if x > 0 then d : ds b x' else []  where (x', d) = divMod x b
-- Reinhard Zumkeller, May 30 2013
  • Mathematica
    Select[Range[700],SubsetQ[IntegerDigits[#,7],IntegerDigits[#,5]]&] (* Harvey P. Dale, Sep 29 2017 *)

A037395 Numbers k such that every base-5 digit of k is a base-8 digit of k.

Original entry on oeis.org

1, 2, 3, 4, 83, 91, 93, 99, 124, 136, 161, 200, 206, 272, 314, 467, 524, 532, 540, 545, 546, 549, 609, 643, 656, 672, 680, 705, 706, 708, 770, 771, 774, 775, 776, 781, 784, 786, 787, 789, 793, 794, 796, 798, 799, 843, 871, 906
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A007091, A007094.
Cf. A037393, A037394, A037396, A037397.

Programs

  • Haskell
    import Data.List ((\\), nub)
a037395 n = a037395_list !! (n-1)
a037395_list = filter f [1..] where
   f x = null $ nub (ds 5 x) \\ nub (ds 8 x)
   ds b x = if x > 0 then d : ds b x' else []  where (x', d) = divMod x b
-- Reinhard Zumkeller, May 30 2013
  • Mathematica
    Select[Range[1000],SubsetQ[IntegerDigits[#,8],IntegerDigits[#,5]]&] (* Harvey P. Dale, Oct 13 2015 *)

A037397 Every base 5 digit of n is a base 10 digit of n.

Original entry on oeis.org

1, 2, 3, 4, 12, 24, 31, 62, 93, 104, 124, 130, 150, 156, 162, 174, 182, 213, 250, 260, 281, 302, 312, 324, 342, 390, 473, 493, 504, 604, 624, 781, 812, 831, 912, 1003, 1030, 1031, 1032, 1033, 1034, 1043, 1083, 1093, 1174, 1234, 1243
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A037393, A037394, A037395, A037396.

Programs

  • Haskell
    import Data.List ((\\), nub)
a037397 n = a037397_list !! (n-1)
a037397_list = filter f [1..] where
   f x = null $ nub (ds 5 x) \\ nub (ds 10 x)
   ds b x = if x > 0 then d : ds b x' else []  where (x', d) = divMod x b
-- Reinhard Zumkeller, May 30 2013

A176722 Primes of the form k^3 + 13, k >= 0.

Original entry on oeis.org

13, 229, 1013, 1741, 39317, 64013, 74101, 157477, 438989, 551381, 830597, 1906637, 2000389, 4096013, 7077901, 9261013, 10941061, 15625013, 16003021, 21024589, 24897101, 27000013, 69934541, 74088013, 79507013, 93576677, 122023949
Offset: 1

Views

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Apr 25 2010

Keywords

Comments

Necessarily, k = 6 * j or k = 6 * j + 4.
Values of k corresponding to terms of the sequence: 0, 6, 10, 12, 34, 40, 42, 54, 76, 82, 94, 124, 126, 160, 192, 210, 222, 250, 252, 276, 292, 300, 412, 420, 430, 454, 496, 502, 570, 586, 612, 622, 640, 670, 684, 712, 720, 724, 726, 756, 784, 822, 826, 874, 882, 894, 934, 952, 964, 1006, 1056.

Examples

			0^3 + 13 = 13 = prime(6) = a(1);
6^3 + 13 = 229 = prime(50) = a(2);
300^3 + 13 = 27000013 = prime(1683067) = a(22).

References

  • H. Rademacher, Topics in Analytic Number Theory, Springer-Verlag Berlin, 1973.

Links

Crossrefs

Cf. A000040, A000578, A037396, A138375, A144953, A154648, A157772, A168147, A168219, A168327.

Programs

  • Magma
    [a: n in [0..500]|IsPrime(a) where a is n^3+13] // Vincenzo Librandi, Dec 22 2010
  • Maple
    select(isprime,[seq(seq((6*j+m)^3+13,m=[0,4]),j=0..1000)]); # Robert Israel, Jun 28 2018
  • Mathematica
    Select[Range[0,1000]^3+13,PrimeQ]  (* Harvey P. Dale, Mar 12 2011 *)

A037432 Positive numbers having the same set of digits in base 5 and base 9.

Original entry on oeis.org

1, 2, 3, 4, 11, 22, 121, 181, 199, 362, 849, 895, 900, 911, 994, 1074, 1084, 1495, 1703, 1711, 1723, 1739, 1794, 1800, 1813, 1822, 2225, 2287, 2288, 2299, 2385, 2469, 2513, 2515, 2945, 3001, 3006, 3034, 3117, 3249, 6582, 6663, 6759, 6761
Offset: 1

Views

Author

Clark Kimberling

Keywords

Examples

			362 is in the sequence because 362 in base 5 is 2422 and in base 9 it is 442.

Links

Crossrefs

Subsequence of A037396.

Programs

  • Mathematica
    Select[Range[7000],Union[IntegerDigits[#,5]]==Union[IntegerDigits[#,9]]&]  (* Harvey P. Dale, Mar 08 2011 *)
  • PARI
    is(n)=Set(digits(n,5))==Set(digits(n,9)) \\ Charles R Greathouse IV, Feb 11 2017

Extensions

More terms from Don Reble, Apr 28 2006
Showing 1-6 of 6 results.

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