A112775 -id:A112775 - cp's OEIS frontend

A112771 Semiprimes of the form 6n + 1.

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

Jonathan Vos Post and Ray Chandler, Oct 15 2005

Union of A108164 and A108166.

Subsequence of A091300. - Zak Seidov, Dec 28 2015

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

IsSemiprime:=func; [s: n in [2..150] | IsSemiprime(s) where s is 6*n + 1]; // Vincenzo Librandi, Sep 22 2012

Select[6 Range[0, 200] + 1, PrimeOmega[#] == 2&] (* Vincenzo Librandi, Sep 22 2012 *)

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

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

Zak Seidov, Mar 14 2017

nonn

Both n and n+1 are terms in A112775.

Robert Israel, Table of n, a(n) for n = 1..10000

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

filter:= n -> numtheory:-bigomega(6*n+1) = 2 and numtheory:-bigomega(6*n+7) = 2:
select(filter, [$1..1000]); # Robert Israel, Dec 23 2024

po[x_]=PrimeOmega[x]; Select[Range[500], po[6# + 1] == po[6# + 7] == 2 &]

for(n=1, 388, if(bigomega(6*n + 1) == 2 && bigomega(6*n + 7) == 2, print1(n,", "))) \\ Indranil Ghosh, Mar 15 2017

A283598 Numbers k such that all three of 6k+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

Zak Seidov, Mar 14 2017

nonn

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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Subsequence of A283597 and A112775.

Cf. A112771, A001358.

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 *)

cp's OEIS Frontend

A112771 Semiprimes of the form 6n + 1.

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

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PARI

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

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cp's OEIS Frontend

A112771 Semiprimes of the form 6n + 1.

Views

Author

Keywords

Comments

Links

Programs

Magma

Mathematica

Formula

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

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