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A284531 Primes p such that 6p - 5 and 6p + 5 are consecutive primes. 1
31, 41, 71, 97, 139, 193, 337, 349, 421, 487, 587, 619, 643, 701, 811, 827, 1021, 1051, 1093, 1217, 1249, 1259, 1471, 1571, 1721, 1747, 1861, 1949, 2087, 2131, 2383, 2521, 2549, 2591, 2957, 3023, 3083, 3209, 3529, 3613, 3779, 3833, 3947, 4283, 4409, 4451, 4481, 4483, 4567, 4591, 4733 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n + 1) = a(n) + 2 for n = 47, 386, 868, 1000, 1247, 1521, 1834, 2271, 2435, 2437, 2468, 2483, 2811, 2819, 2960, 3202, 3531, 3581, 5021, 5178, 5245, 5669, 6009, 6087, 6198, 6686, 7017, 7029, 7454, 7576, 7699, 8557, 8940, 9018, 10130, 10240, 10449, 10578, 10952, 11070, 11103, 11199, ...

E.g., a(42)=4481 and a(43)=4483.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

31*6 - 5 = 181 = A000040(42) and 31*6 + 5 = 191 = A000040(43).

MAPLE

filter:= p -> isprime(p) and isprime(6*p-5) and isprime(6*p+5) and not isprime(6*p-1) and not isprime(6*p+1):

select(filter, [seq(i, i=3..10000, 2)]); # Robert Israel, Apr 07 2017

MATHEMATICA

Select[Range[31, 5000, 2], PrimeQ[#] && PrimeQ[a = 6 # - 5] && NextPrime[a] == a + 10 &]

cp6Q[n_]:=Module[{p1=6n-5}, PrimeQ[p1]&&NextPrime[p1]==6n+5]; Select[ Prime[ Range[ 1000]], cp6Q] (* Harvey P. Dale, Jun 05 2017 *)

CROSSREFS

Subsequence of A127430. Cf. A000040.

Sequence in context: A285805 A141180 A176371 * A040987 A040180 A158754

Adjacent sequences:  A284528 A284529 A284530 * A284532 A284533 A284534

KEYWORD

nonn

AUTHOR

Zak Seidov, Mar 28 2017

STATUS

approved

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Last modified September 15 18:22 EDT 2019. Contains 327082 sequences. (Running on oeis4.)