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.

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A153309 Numbers k such that 3*k + 1 is not prime.

Original entry on oeis.org

0, 1, 3, 5, 7, 8, 9, 11, 13, 15, 16, 17, 18, 19, 21, 23, 25, 27, 28, 29, 30, 31, 33, 35, 37, 38, 39, 40, 41, 43, 44, 45, 47, 48, 49, 51, 53, 55, 56, 57, 58, 59, 61, 62, 63, 65, 67, 68, 69, 71, 72, 73, 75, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 91, 93, 95
Offset: 1

Views

Author

Vincenzo Librandi, Dec 23 2008

Keywords

Comments

Terms (except 0) can be written as 3xy +- (x + y) for x > 0, y > 0. - Ron R Spencer, Aug 01 2016
Apart from a(2) = 1 the sequence comprises those numbers k such that (3*k)!/(3*k + 1) is an integer. - Peter Bala, Jan 25 2017

Examples

			Distribution of the even terms in the following triangular array:
                        *;
                      *   8;
                    *   *  16;
                  *   *   *   *;
                *  18   *   *  40;
              *   *  30   *   *  56;
            *   *   *   *   *   *   *;
          *  28   *   *  62   *   *  96;
        *   *  44   *   *  82   *   *  120;
      *   *   *   *   *   *   *   *   *   *;
    *  38   *   *  84   *   *  130  *   *  176;
  *   *  58   *   *  108  *   *  158  *   *  208;
etc., where * marks the noninteger values of (4*h*k + 2*k + 2*h)/3 with h >= k >= 1. - _Vincenzo Librandi_, Jan 17 2013

Links

Crossrefs

Cf. A024892, A014076, A153170, A045751, A095277, A153088, A153329, A153343.

Programs

  • Magma
    [n: n in [0..150] | not IsPrime(3*n + 1)]; // Vincenzo Librandi, Jan 12 2013
  • Maple
    # produces the sequence apart from the term equal to 1
for n from 0 to 100 do
if irem(factorial(3*n), 3*n+1) = 0 then print(n); end if;
end do: # Peter Bala, Jan 25 2017
  • Mathematica
    Select[Range[0, 200], !PrimeQ[3*# + 1]&] (* Vincenzo Librandi, Jan 12 2013 *)
  • PARI
    is(n)=!isprime(3*n+1) \\ Charles R Greathouse IV, Aug 01 2016

Extensions

Erroneous comment deleted by N. J. A. Sloane, Jun 23 2010
0 added by Arkadiusz Wesolowski, Jun 25 2011

A333721 Numbers k such that k + 1, 2k + 1, 3k + 1, 4k + 1, and 6k + 1 are all prime.

Original entry on oeis.org

1530, 4260, 25410, 26040, 78540, 111720, 174990, 211050, 214830, 395430, 403260, 409290, 459690, 487830, 512820, 711120, 779790, 910560, 1023750, 1135950, 1280370, 1312350, 1451520, 1464810, 1487070, 1563510, 1623360, 1698060, 1824330, 1933680, 2006340, 2097480
Offset: 1

Views

Author

Pedro Caceres, May 04 2020

Keywords

Comments

All terms are multiples of 6.
All terms are multiples of 30. - Robert Israel, Jun 17 2020

Examples

			25410 is in the sequence because 25411, 50821, 76231, 101641, 152461 are all prime.

Links

Crossrefs

Cf. A006093, A005097, A024892, A087370, A005098, A005099, A024898, A024899.

Programs

  • Maple
    select(t -> andmap(isprime, [t+1,2*t+1,3*t+1,4*t+1,6*t+1]), [seq(i,i=30..3*10^6,30)]); # Robert Israel, Jun 17 2020
  • PARI
    isok(m)={for(i=1, 6, if(i<>5&&!isprime(i*m+1), return(0))); 1}
{ forstep(n=0, 3*10^6, 6, if(isok(n), print1(n, ", "))) } \\ Andrew Howroyd, May 04 2020

A366931 Least k such that 3*n*k+1 is a prime.

Original entry on oeis.org

2, 1, 2, 1, 2, 1, 2, 3, 4, 1, 2, 1, 2, 1, 4, 2, 2, 2, 4, 1, 2, 1, 2, 1, 2, 1, 2, 4, 4, 2, 4, 1, 2, 1, 2, 1, 2, 2, 8, 2, 6, 1, 8, 3, 2, 1, 2, 3, 6, 1, 2, 1, 20, 1, 2, 2, 12, 2, 4, 1, 2, 2, 2, 1, 6, 1, 8, 2, 4, 1, 4, 2, 2, 1, 8, 1, 2, 4, 6, 1, 2, 3, 2, 3, 4, 4
Offset: 1

Views

Author

Robert Price, Dec 17 2023

Keywords

Links

Crossrefs

Cf. A016014, A024892.
A070847 lists the corresponding primes.

Programs

  • Mathematica
    A366931 = {};
Do[k=1; While[!PrimeQ[3 n k+1], k++]; AppendTo[A366931 ,k], {n,85}];
A366931
lkp[n_]:=Module[{k=1},While[!PrimeQ[3n*k+1],k++];k]; Array[lkp,90] (* Harvey P. Dale, Jan 09 2025 *)
  • PARI
    a(n) = my(k=1); while (!isprime(3*n*k+1), k++); k; \\ Michel Marcus, Dec 17 2023
Previous Showing 11-13 of 13 results.

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

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