

A255607


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


3



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
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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



