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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A381465 Semiprimes k such that 6*k + 1 is also a semiprime.

Original entry on oeis.org

4, 9, 14, 15, 22, 34, 39, 49, 65, 69, 74, 82, 85, 86, 93, 94, 111, 133, 145, 158, 159, 183, 185, 194, 201, 203, 209, 214, 219, 226, 235, 259, 265, 267, 289, 299, 301, 303, 319, 321, 323, 326, 327, 334, 341, 346, 358, 361, 362, 365, 371, 377, 386, 393, 403, 407, 413, 415, 422, 427, 437, 469, 471
Offset: 1

Views

Author

Zak Seidov and Robert Israel, Feb 24 2025

Keywords

Examples

			a(3) = 14 is a term because 14 = 2 * 7 is a semiprime and 6 * 14 + 1 = 85 = 5 * 17 is also a semiprime.

Links

Crossrefs

Cf. A001358, A007693, A111153, A111170.

Programs

  • Maple
    select(t -> numtheory:-bigomega(t) = 2 and numtheory:-bigomega(6*t+1)=2, [$4..1000]);
  • Mathematica
    s = {}; Do[If[{2, 2} == PrimeOmega[{k, 6*k + 1}], AppendTo[s, k]], {k, 1000}] ; s
  • PARI
    isok(k) = (bigomega(k)==2) && (bigomega(6*k+1)==2); \\ Michel Marcus, Feb 26 2025

A106060 Primes p such that 1*p + 8 and 8*p + 1 are primes.

Original entry on oeis.org

5, 11, 29, 71, 101, 131, 149, 269, 401, 431, 449, 479, 491, 599, 761, 821, 929, 1229, 1289, 1559, 1571, 1601, 1619, 1871, 2081, 2129, 2339, 2531, 2549, 2609, 2741, 3041, 3209, 3299, 3461, 3719, 3761, 4289, 5189, 5861, 6269, 6359, 6569, 6701, 6959, 7211
Offset: 1

Views

Author

Zak Seidov, May 07 2005

Keywords

Comments

Cf. A045536: Primes p such that 1*p+2 and 2*p+1 are prime; A007693: Numbers n such that n and 6*n+1 are primes.

Crossrefs

Cf. A007693, A045536.

Programs

  • Magma
    [p: p in PrimesUpTo(10000) | IsPrime(p+8) and IsPrime(8*p+1)]; // Vincenzo Librandi, Nov 13 2010
  • Mathematica
    Select[Prime[Range[220]], PrimeQ[8#+1]&&PrimeQ[1#+8]&]

A173230 Primes p of the form 6k+1 such that 6p+1 is also prime.

Original entry on oeis.org

7, 13, 37, 61, 73, 103, 151, 181, 241, 271, 277, 283, 313, 331, 367, 373, 397, 577, 601, 607, 661, 727, 751, 787, 853, 907, 937, 1033, 1063, 1117, 1171, 1201, 1321, 1327, 1381, 1423, 1453, 1531, 1567, 1693, 1777, 1831, 1873, 1987, 1993, 2137, 2161, 2203, 2221, 2281, 2287, 2293, 2347, 2551, 2593, 2677, 2767, 2791, 2851, 2971, 3037, 3061, 3163, 3181, 3307, 3391
Offset: 1

Views

Author

Zak Seidov, Nov 22 2010

Keywords

Crossrefs

Subsequence of A007693 which in turn is subsequence of A024899.

Programs

  • Magma
    [ p: n in [0..600] | IsPrime(6*p+1) and IsPrime(p) where p is 6*n+1 ];
  • Mathematica
    sp1Q[n_]:=IntegerQ[(n-1)/6]&&PrimeQ[6n+1]; Select[Prime[Range[500]],sp1Q] (* Harvey P. Dale, Apr 08 2018 *)
Previous Showing 21-23 of 23 results.

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

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