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A022546 Initial members of prime nonuplets (p, p+2, p+6, p+12, p+14, p+20, p+24, p+26, p+30). 30
17, 1277, 113147, 252277007, 408936947, 521481197, 1116452627, 1209950867, 1645175087, 2966003057, 3947480417, 6234613727, 9307040837, 9853497737, 11878692167, 13766391467, 21956291867, 22741837817, 24388061207 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subsequence of A022012. - R. J. Mathar, Feb 10 2013

All terms congruent to 17 (modulo 30). - Matt C. Anderson, May 27 2015

LINKS

Matt C. Anderson and Dana Jacobsen, Table of n, a(n) for n = 1..10000 [first 200 terms from Matt C. Anderson]

T. Forbes, Prime k-tuplets

MAPLE

composite_small := proc (n::integer)

description "determine if n has a prime factor less than 100";

if igcd(2305567963945518424753102147331756070, n) = 1 then return false else return true;

end if ;

end proc:

p := [0, 2, 6, 12, 14, 20, 24, 26, 30]:

# using isprime(m*n+o+p)

o := 17:

m:=30:

loopstop:=10^11:

loopstart:=0:

for n from loopstart to loopstop do

counter := 0:

wc := 0;

wd := 0;

while `and`(wd > -10, wd < 9) do

wd := wd+1;

if composite_small(m*n+o+p[wd]) = false then wd := wd+1 else wd := -10 end if ;

end do;

if wd >= 9 then

while `and`(counter >= 0, wc < 9) do

wc := wc+1;

if isprime(m*n+o+p[wc]) then counter := counter+1 else counter := -1 end if;

end do end if;

if counter = 9 then print(m*n+o) end if;

end do:

MATHEMATICA

Select[Prime[Range[260000000]], Union[PrimeQ[ # +{2, 6, 12, 14, 20, 24, 26, 30}]]=={True} &] (* Vincenzo Librandi, May 27 2015 *)

PROG

(MAGMA) [p: p in PrimesUpTo(260000000) | forall{p+r: r in [2, 6, 12, 14, 20, 24, 26, 30] | IsPrime(p+r)}]; // Vincenzo Librandi, May 27 2015

(Perl) use ntheory ":all"; say for sieve_prime_cluster(1, 1e11, 2, 6, 12, 14, 20, 24, 26, 30); # Dana Jacobsen, Sep 30 2015

(PARI) forprime(p=2, 1e30, if (isprime(p+2) && isprime(p+6) && isprime(p+12) && isprime(p+14) && isprime(p+20) && isprime(p+24) && isprime(p+26) && isprime(p+30) , print1(p", "))) \\ Altug Alkan, Sep 30 2015

CROSSREFS

Sequence in context: A305872 A172456 A022012 * A268067 A188717 A266866

Adjacent sequences:  A022543 A022544 A022545 * A022547 A022548 A022549

KEYWORD

nonn

AUTHOR

Warut Roonguthai

STATUS

approved

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Last modified May 9 05:40 EDT 2021. Contains 343688 sequences. (Running on oeis4.)