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 1-5 of 5 results.

A112775 Numbers k such that 6k+1 is semiprime.

Original entry on oeis.org

4, 8, 9, 14, 15, 19, 20, 22, 24, 28, 31, 34, 36, 39, 41, 42, 43, 44, 48, 49, 50, 53, 59, 60, 65, 67, 69, 71, 74, 75, 78, 80, 82, 84, 85, 86, 88, 89, 92, 93, 94, 97, 98, 108, 109, 111, 113, 114, 116, 117, 120, 124, 127, 130, 132, 133, 136, 139, 140, 144, 145, 148, 149
Offset: 1

Views

Author

Jonathan Vos Post and Ray Chandler, Oct 15 2005

Keywords

Links

Crossrefs

Cf. A112771 (resulting semiprimes).

Programs

  • Magma
    IsSemiprime:=func; [n: n in [2..150] | IsSemiprime(6*n+1)]; // Vincenzo Librandi, Sep 22 2012
  • Mathematica
    Select[Range[200],Plus@@Last/@FactorInteger[6#+1]==2&] (* Vincenzo Librandi, Sep 22 2012 *)

Formula

a(n) = (A112771(n) - 1)/6.

A283597 Numbers n such that both 6n+1 and 6n+7 are semiprimes.

Original entry on oeis.org

8, 14, 19, 41, 42, 43, 48, 49, 59, 74, 84, 85, 88, 92, 93, 97, 108, 113, 116, 132, 139, 144, 148, 149, 157, 158, 159, 162, 163, 189, 190, 193, 198, 209, 210, 211, 222, 223, 224, 225, 226, 227, 231, 234, 235, 250, 251, 259, 264, 272, 280, 285, 306, 307, 315, 316, 317, 318, 319, 320, 323, 326, 327, 340, 345, 349, 358, 361, 368, 376, 386, 387, 388
Offset: 1

Views

Author

Zak Seidov, Mar 14 2017

Keywords

Comments

Both n and n+1 are terms in A112775.

Links

Crossrefs

Cf. A112771 (6n+1 semiprimes), A112775 (6n+1 is semiprime), A001358 (semiprimes).

Programs

  • Maple
    filter:= n -> numtheory:-bigomega(6*n+1) = 2 and numtheory:-bigomega(6*n+7) = 2:
select(filter, [$1..1000]); # Robert Israel, Dec 23 2024
  • Mathematica
    po[x_]=PrimeOmega[x]; Select[Range[500], po[6# + 1] == po[6# + 7] == 2 &]
  • PARI
    for(n=1, 388, if(bigomega(6*n + 1) == 2 && bigomega(6*n + 7) == 2, print1(n,", "))) \\ Indranil Ghosh, Mar 15 2017

A344872 Semiprimes of the form 3m+2.

Original entry on oeis.org

14, 26, 35, 38, 62, 65, 74, 77, 86, 95, 119, 122, 134, 143, 146, 155, 158, 161, 185, 194, 203, 206, 209, 215, 218, 221, 254, 278, 287, 299, 302, 305, 314, 323, 326, 329, 335, 341, 362, 365, 371, 377, 386, 395, 398, 407, 413, 422, 437, 446, 458, 473, 482, 485, 497
Offset: 1

Views

Author

Peter Munn, May 31 2021

Keywords

Comments

There are no square terms, as squares are congruent to 0 or 1 modulo 3.
Products of a prime of the form 3m+1 and a prime of the form 3m+2 (the former necessarily being of the form 6m+1).

Examples

			14 = 2 * 7 has 2 prime factors (counting repetitions) so is a semiprime, and 14 = 3*4 + 2, so has the form 3m+2. So 14 is in the sequence.

Crossrefs

Intersection of A001358 and A016789.
Disjoint union of A108172 and A112772.
Complement within A001358 of A001748, A112771 and A112774.
Subsequence of A344703.

Programs

  • Mathematica
    Select[Range[2,500,3],PrimeOmega@#==2&] (* Giorgos Kalogeropoulos, Jun 02 2021 *)
  • PARI
    isok(m) = bigomega(m) == 2 && m % 3 == 2;

A283598 Numbers k such that all three of 6*k+1, 6*(k+1)+1, and 6*(k+2)+1 are semiprimes.

Original entry on oeis.org

41, 42, 48, 84, 92, 148, 157, 158, 162, 189, 209, 210, 222, 223, 224, 225, 226, 234, 250, 306, 315, 316, 317, 318, 319, 326, 386, 387, 401, 407, 408, 433, 462, 487, 488, 489, 514, 515, 521, 532, 539, 566, 567, 568, 569, 580, 598, 633, 634, 662, 663, 664, 672, 697, 713, 717, 718
Offset: 1

Views

Author

Zak Seidov, Mar 14 2017

Keywords

Comments

That is, k, k+1 and k+2 are terms in A112775.

Links

Crossrefs

Subsequence of A283597 and A112775.
Cf. A112771, A001358.

Programs

  • Mathematica
    po[x_]=PrimeOmega[x];Select[Range[1000],po[6*#+1]==po[6*(1+#)+1]==po[6*(2+#)+1]==2 &]
Select[Range[800],PrimeOmega[6#+{1,7,13}]=={2,2,2}&] (* Harvey P. Dale, Apr 23 2024 *)

A343670 a(n) is the least semiprime congruent to 1 (mod n-th semiprime).

Original entry on oeis.org

9, 25, 10, 21, 15, 46, 22, 111, 26, 183, 34, 35, 106, 39, 118, 93, 295, 205, 111, 58, 291, 187, 326, 346, 371, 155, 247, 86, 87, 262, 183, 94, 95, 381, 213, 334, 346, 119, 358, 122, 123, 247, 259, 134, 403, 142, 143, 287, 146, 731, 466, 159, 319, 323, 831, 339, 178, 535, 1099, 371, 562
Offset: 1

Views

Author

Zak Seidov, May 09 2021

Keywords

Examples

			9 = 4*2+1, 25 = 6*4+1, 10 = 9*1+1.

Crossrefs

Cf. A001358, A108181, A112771.

Programs

  • Mathematica
    sp = Select[Range[4, 10^3], 2 == PrimeOmega[#] &]; Table[n = sp[[k]]; a = n; While[2 != PrimeOmega[a + 1], a = a + n]; a + 1, {k, 100}]
Showing 1-5 of 5 results.

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

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