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 1-9 of 9 results.

A112771 Semiprimes of the form 6n + 1.

Original entry on oeis.org

25, 49, 55, 85, 91, 115, 121, 133, 145, 169, 187, 205, 217, 235, 247, 253, 259, 265, 289, 295, 301, 319, 355, 361, 391, 403, 415, 427, 445, 451, 469, 481, 493, 505, 511, 517, 529, 535, 553, 559, 565, 583, 589, 649, 655, 667, 679, 685, 697, 703, 721, 745
Offset: 1

Views

Author

Jonathan Vos Post and Ray Chandler, Oct 15 2005

Keywords

Comments

Union of A108164 and A108166.
Subsequence of A091300. - Zak Seidov, Dec 28 2015

Links

Programs

  • Magma
    IsSemiprime:=func; [s: n in [2..150] | IsSemiprime(s) where s is 6*n + 1]; // Vincenzo Librandi, Sep 22 2012
  • Mathematica
    Select[6 Range[0, 200] + 1, PrimeOmega[#] == 2&] (* Vincenzo Librandi, Sep 22 2012 *)

Formula

a(n) = 6 * A112775(n) +1.

A291745 Nonprimes of the form 3*k + 1.

Original entry on oeis.org

1, 4, 10, 16, 22, 25, 28, 34, 40, 46, 49, 52, 55, 58, 64, 70, 76, 82, 85, 88, 91, 94, 100, 106, 112, 115, 118, 121, 124, 130, 133, 136, 142, 145, 148, 154, 160, 166, 169, 172, 175, 178, 184, 187, 190, 196, 202, 205, 208, 214, 217, 220, 226, 232, 235, 238, 244, 247
Offset: 1

Views

Author

Vincenzo Librandi, Aug 31 2017

Keywords

Comments

Subsequence of A018252. A091300 is a subsequence.
A multiplicative semigroup: if m and n are in the sequence, then so is m*n. - Antti Karttunen, Jul 02 2024

Links

Crossrefs

Cf. A002476, A016777, A091113, A091300, A291746, A291747, A373977 (characteristic function).

Programs

  • Magma
    [n: n in [1..400 by 3] | not IsPrime(n)];
  • Mathematica
    DeleteCases[3 Range[0, 300] + 1, _?PrimeQ]

A092256 Nonprimes of form 6k+5.

Original entry on oeis.org

35, 65, 77, 95, 119, 125, 143, 155, 161, 185, 203, 209, 215, 221, 245, 275, 287, 299, 305, 323, 329, 335, 341, 365, 371, 377, 395, 407, 413, 425, 437, 455, 473, 485, 497, 515, 527, 533, 539, 545, 551, 575, 581, 605, 611, 623, 629, 635, 665, 671, 689, 695
Offset: 1

Views

Author

Labos Elemer, Feb 24 2004

Keywords

Links

Crossrefs

Cf. A091113, A091300.

Programs

  • Maple
    for k from 0 to 100 do if(not isprime(6*k+5))then printf("%d, ",6*k+5); fi: od: # Nathaniel Johnston, May 18 2011
  • Mathematica
    Do[If[ !PrimeQ[n]&&Equal[Mod[n, 6], 5 ], Print[n]], {n, 1, 1000}]
Select[6*Range[150]+5,!PrimeQ[#]&] (* Harvey P. Dale, Jan 23 2012 *)

A199859 Numbers k such that 6k-5 is a composite number of the form (6x-5)*(6y-5) when x or y is not equal to 1 except for k=1.

Original entry on oeis.org

1, 9, 16, 23, 29, 30, 37, 42, 44, 51, 55, 58, 61, 65, 68, 72, 79, 80, 81, 86, 93, 94, 99, 100, 105, 107, 114, 118, 120, 121, 128, 130, 133, 135, 137, 142, 146, 149, 155, 156, 159, 161, 163, 170, 172, 175, 177, 180, 184, 185, 191, 192, 194, 198, 205, 211, 212
Offset: 0

Views

Author

Eleonora Echeverri-Toro, Nov 11 2011

Keywords

Comments

Numbers whose associate in A091300 has at least one nontrivial factorization into two factors of A016921.

Crossrefs

Cf. A091300.

Programs

  • Maple
    isA016921 := proc(n)
    (n mod 6)=1 ;
end proc:
isA091300 := proc(n)
    (not isprime(n)) and isA016921(n) ;
end proc:
isA199859 := proc(n)
    if n = 1 then
        return true;
    elif isA091300(6*n-5) then
        for d in numtheory[divisors](6*n-5) minus {1,6*n-5} do
            if isA016921(d) and isA016921((6*n-5)/d) then
                return true;
            end if;
        end do:
        return false;
    else
        return false;
    end if;
end proc:
for n from 1 to 210 do
    if isA199859(n) then
        printf("%d,",n) ;
    end if ;
end do; # R. J. Mathar, Nov 25 2011

A291746 Nonprimes of the form 5*k + 1.

Original entry on oeis.org

1, 6, 16, 21, 26, 36, 46, 51, 56, 66, 76, 81, 86, 91, 96, 106, 111, 116, 121, 126, 136, 141, 146, 156, 161, 166, 171, 176, 186, 196, 201, 206, 216, 221, 226, 231, 236, 246, 256, 261, 266, 276, 286, 291, 296, 301, 306, 316, 321, 326, 336, 341, 346, 351, 356, 361, 366, 371
Offset: 1

Views

Author

Vincenzo Librandi, Aug 31 2017

Keywords

Comments

Subsequence of A018252.

Crossrefs

Cf. A016861, A030430, A091113, A091300, A291745, A291747.

Programs

  • Magma
    [n: n in [1..400 by 5] | not IsPrime(n)];
  • Mathematica
    DeleteCases[5 Range[0, 200] + 1, _?PrimeQ]

A291747 Nonprimes of the form 7*k + 1.

Original entry on oeis.org

1, 8, 15, 22, 36, 50, 57, 64, 78, 85, 92, 99, 106, 120, 134, 141, 148, 155, 162, 169, 176, 183, 190, 204, 218, 225, 232, 246, 253, 260, 267, 274, 288, 295, 302, 309, 316, 323, 330, 344, 351, 358, 365, 372, 386, 393, 400, 407, 414, 428, 435, 442, 456, 470, 477, 484, 498
Offset: 1

Views

Author

Vincenzo Librandi, Aug 31 2017

Keywords

Comments

Subsequence of A018252.

Crossrefs

Cf. A016993, A091113, A091300, A140444, A291745, A291746.

Programs

  • Magma
    [n: n in [1..500 by 7] | not IsPrime(n)];
  • Mathematica
    DeleteCases[7 Range[0, 200] + 1, _?PrimeQ]

A175521 Nonprimes k such that 9*k divides 2^(k-1) - 1.

Original entry on oeis.org

1, 1105, 1387, 1729, 2047, 2701, 2821, 3277, 4033, 4369, 4681, 5461, 6601, 7957, 8911, 10261, 10585, 11305, 13741, 13747, 13981, 14491, 15709, 15841, 16705, 18721, 19951, 23377, 29341, 30121, 30889, 31417, 31609, 31621, 34945, 39865, 41041, 41665, 42799, 46657, 49141, 49981
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Dec 18 2010

Keywords

Comments

Original name was: Nonprimes n of the form 6m+1 such that (2^(n-1) mod n)=(4^(n-1) mod n)=(8^(n-1) mod n)=..=(k^(n-1) mod n) for k=2,4,8,..,smallest power of 2>n.

Examples

			1 is a term because it is a nonprime and 9*1 = 9 divides 2^(1-1) - 1 = 0.

Links

Crossrefs

Subsequence of A001567.
Cf. A000079, A091300.

Programs

  • Mathematica
    n = 1; t = {}; While[Length[t] < 100, While[PrimeQ[n] || PowerMod[2, n-1, 9*n] != 1, n = n + 2]; AppendTo[t, n]; n = n + 2]; t (* T. D. Noe, Jul 25 2011 *)
  • PARI
    p=0;forprime(q=2,1e5,for(n=p+1,q-1,if(Mod(2,9*n)^(n-1)==1,print1(n", ")));p=q) \\ Charles R Greathouse IV, Jul 24 2011

Extensions

Name changed by Arkadiusz Wesolowski, Jul 23 2011

A172181 Odd composites not of the form 6k + 1.

Original entry on oeis.org

9, 15, 21, 27, 33, 35, 39, 45, 51, 57, 63, 65, 69, 75, 77, 81, 87, 93, 95, 99, 105, 111, 117, 119, 123, 125, 129, 135, 141, 143, 147, 153, 155, 159, 161, 165, 171, 177, 183, 185, 189, 195, 201, 203, 207, 209, 213, 215, 219, 221, 225, 231, 237, 243, 245, 249, 255
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jan 28 2010

Keywords

Crossrefs

Cf. A005408, A045375, A045410. Odd complement is A091300.

Programs

  • Mathematica
    Union[6Range[42] + 3, Select[6Range[43] - 1, Not[PrimeQ[#]] &]] (* Alonso del Arte, Jun 05 2011 *)
  • PARI
    select(n->(n%6==3 && n>3) || (n%6==5 && !isprime(n)), vector(1000,i,i)) \\ Charles R Greathouse IV, Jun 05 2011

Extensions

Entries checked by R. J. Mathar, May 19 2010

A199860 Numbers k such that 6k-5 is a composite number of the form (6x-1) * (6y-1).

Original entry on oeis.org

5, 10, 15, 20, 21, 25, 30, 32, 35, 40, 43, 45, 49, 50, 54, 55, 60, 65, 66, 70, 75, 76, 80, 83, 85, 87, 89, 90, 95, 98, 100, 105, 109, 110, 112, 115, 117, 120, 125, 130, 131, 134, 135, 140, 141, 142, 145, 150, 151, 153, 155, 158, 160, 164, 165, 168, 170, 175
Offset: 1

Views

Author

Eleonora Echeverri-Toro, Nov 11 2011

Keywords

Comments

Numbers whose associate in A091300 has at least one factorization into two factors of A016969.

Examples

			n=5 is in the sequence because 6*5-5 = 25 = 5*5 with x = y = 1.
n=10 is in the sequence because 6*10-5 = 55 = 5*11 with x=1, y=2.

Crossrefs

Cf. A199859.

Programs

  • Maple
    isA016969 := proc(n)
    (n mod 6)=5 ;
end proc:
isA016921 := proc(n)
    (n mod 6)=1 ;
end proc:
isA091300 := proc(n)
    (not isprime(n)) and isA016921(n) ;
end proc:
isA199860 := proc(n)
    if isA091300(6*n-5) then
        for d in numtheory[divisors](6*n-5) minus {1} do
            if isA016969(d) and isA016969((6*n-5)/d) then
                return true;
            end if;
        end do:
        return false;
    else
        return false;
    end if;
end proc:
for n from 5 to 210 do
    if isA199860(n) then
        printf("%d,",n) ;
    end if ;
end do; # R. J. Mathar, Nov 27 2011
Showing 1-9 of 9 results.

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