A255607 Numbers n such that both 4*n+1 and 6*n+1 are primes.

1, 3, 7, 10, 13, 18, 25, 27, 37, 45, 58, 70, 73, 87, 100, 102, 105, 112, 115, 135, 142, 153, 165, 168, 175, 177, 192, 202, 205, 213, 220, 238, 255, 258, 277, 282, 298, 300, 312, 322, 325, 352, 357, 363, 370, 373, 417, 423, 447, 465, 472, 475, 513, 520

Offset: 1

Author

Vincenzo Librandi, Feb 28 2015

Keywords

• nonn
• easy

Comments

Numbers n such that A033570(2n) is semiprime.

Examples

			10 is in this sequence because 4*10+1=41 and 6*10+1=61 are primes.
		

Links

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

Crossrefs

Cf. A001358, A033570, A130800, A186721.

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

Programs

Magma

[n: n in [1..600] | IsPrime(6*n+1) and IsPrime(4*n+1)];

Maple

A255607:=n->`if`(isprime(4*n+1) and isprime(6*n+1), n, NULL): seq(A255607(n), n=1..600); # Wesley Ivan Hurt, Feb 28 2015

Mathematica

Select[Range[600], PrimeQ[4 # + 1] && PrimeQ[6 # + 1] &]
Select[Range[600],AllTrue[{4#,6#}+1,PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 22 2020 *)

PARI

for(n=1,10^3,if(isprime(4*n+1)&&isprime(6*n+1),print1(n,", "))) \\ Derek Orr, Mar 01 2015

PARI

select( is_A255607(n)=isprime(4*n+1)&&isprime(6*n+1), [1..555]) \\ M. F. Hasler, Dec 13 2019

Formula

a(n) = A130800(n)/2.