A255607 -id:A255607 - cp's OEIS frontend

A130800 Numbers k such that both 2k+1 and 3k+1 are primes.

2, 6, 14, 20, 26, 36, 50, 54, 74, 90, 116, 140, 146, 174, 200, 204, 210, 224, 230, 270, 284, 306, 330, 336, 350, 354, 384, 404, 410, 426, 440, 476, 510, 516, 554, 564, 596, 600, 624, 644, 650, 704, 714, 726, 740, 746, 834, 846, 894, 930, 944, 950, 1026, 1040

Offset: 1

Max Alekseyev, Jul 18 2007

nonn

Also: k such that A033570(k) is semiprime. All terms are congruent to 0 or 2 modulo 6. - M. F. Hasler, Dec 13 2019

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

Intersection of A005097 and A024892. - M. F. Hasler, Dec 13 2019

Cf. A033570; A255584: semiprimes of the form (4*n+1)*(6*n+1).

[n: n in [0..500] | IsPrime(2*n+1) and IsPrime(3*n+1)]; // Vincenzo Librandi, Nov 23 2010

Select[Range[1100],AllTrue[{2,3}#+1,PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 17 2016 *)

select( is_A130800(n)=isprime(2*n+1)&&isprime(3*n+1), [1..1111]) \\ M. F. Hasler, Dec 13 2019

a(n) = 2*A255607(n). - M. F. Hasler, Dec 13 2019

More terms from Vincenzo Librandi, Mar 26 2010

A255584 Semiprimes of the form (4n + 1)(6n + 1) = 24n^2 + 10*n + 1.

Original entry on oeis.org

35, 247, 1247, 2501, 4187, 7957, 15251, 17767, 33227, 49051, 81317, 118301, 128627, 182527, 241001, 250717, 265651, 302177, 318551, 438751, 485357, 563347, 655051, 679057, 736751, 753667, 886657, 981317, 1010651, 1090987, 1163801, 1361837, 1563151

Offset: 1

Vincenzo Librandi, Feb 27 2015

nonn

The first few values of n such that both n and n+1 give semiprimes in the sequence begin: 2607, 4017, 4062, 5967, 7107, 8472, 8892, ... In such cases, numbers of the form 10n+8 can always be expressed as the sum of the two primes 4n+1 and 6n+7. - Wesley Ivan Hurt, Feb 27 2015

			35 is in the sequence because 35 = 5*7 and 5, 7 are primes of the form 4*k+1 and 6*k+1 respectively.
247 is in the sequence because 247 = 13*19: both 13, 19 are primes of the form 6*k+1 and 13 also has the form 4*k+1.

Subsequence of A245365.
Cf. A001358, A002144, A002476, A113941, A255607 (associated n).
Equals A033570(A130800). - M. F. Hasler, Dec 13 2019

[(4*n+1)*(6*n+1): n in [1..300] | IsPrime(4*n+1) and IsPrime(6*n+1)];

IsSemiprime:=func; [s: n in [1..300] | IsSemiprime(s) where s is 24*n^2+10*n+1];

Select[Table[24 n^2 + 10 n + 1, {n, 300}], PrimeOmega[#] == 2 &] (* or *) f[n_] := Last /@ FactorInteger[n] == {1, 1}; Select[Array[24 #^2 + 10 # + 1 &, 300], f[#] &]

for(n=1,250,if(bigomega(s=24*n^2+10*n+1)==2,print1(s,", "))) \\ Derek Orr, Feb 28 2015

a(n) = A033570(A130800(n)) = A033570(2*A255607(n)). - M. F. Hasler, Dec 13 2019

cp's OEIS Frontend

A130800 Numbers k such that both 2k+1 and 3k+1 are primes.

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A255584 Semiprimes of the form (4n + 1)(6n + 1) = 24n^2 + 10*n + 1.

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cp's OEIS Frontend

A130800 Numbers k such that both 2k+1 and 3k+1 are primes.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

Extensions

A255584 Semiprimes of the form (4*n + 1)*(6*n + 1) = 24*n^2 + 10*n + 1.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Magma

Magma

Mathematica

PARI

Formula

A255584 Semiprimes of the form (4n + 1)(6n + 1) = 24n^2 + 10*n + 1.