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

1,2

Comments

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

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A001358, A033570, A130800, A186721.

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

Sequence in context: A198267 A298786 A285359 * A310185 A339620 A319241

Adjacent sequences: A255604 A255605 A255606 * A255608 A255609 A255610

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 28 2015

Status

approved