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A286915 Primes p such that p+6, p+12, p+18, p+20, p+26, p+32, and p+38 are all primes 1
41, 344231, 1464251, 9646271, 48691151, 53544461, 58182011, 68632121, 74656931, 74752571, 92195381, 122898851, 164527151, 204214541, 224671901, 233766041, 234327701, 269106731, 349373891, 396416711, 412572851, 448517501, 513644381, 530427071, 559946021 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Many, but not all, of the terms are the smallest prime in a sequence of 8 consecutive primes with first differences equal to 6, 6, 6, 2, 6, 6, 6. -Harvey P. Dale, May 24 2017

Of the first 400 terms, 311 are the smallest prime in a sequence of 8 consecutive primes with first differences equal to 6, 6, 6, 2, 6, 6, 6. - Harvey P. Dale_, May 25, 2017

All terms are congruent to 11 mod 30. - Zak Seidov_, May 24, 2017 [Proof: Suppose p == x mod 30. Then all of x, x+6, x+12, x+18, x+20, x+26, x+2, and x+8 must be relatively prime to 30. This implies x = 11. (We cannot have x=1, for then p+2 would be == 3 mod 30, we cannot have x=7, for then p+18 would be == 25 mod 30, and so on.) - N. J. A. Sloane, May 24 2017]

REFERENCES

Zak Seidov, posting to the Sequence Fans Mailing List, May 21, 2017.

Peter Munn, postings to the Sequence Fans Mailing List, May 22 and 24, 2017.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..400

EXAMPLE

9646271 is included because 9646277, 9646283, 9646289, 9646291, 9646297, 9646303, and 9646309 are all primes.

MATHEMATICA

Select[Prime[Range[10^7]], AllTrue[#+{6, 12, 18, 20, 26, 32, 38}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *)

Select[{41, 251, 311}+#&/@(330*Range[0, 1000000])//Flatten, AllTrue[#+{0, 6, 12, 18, 20, 26, 32, 38}, PrimeQ]&] (* Much faster than the first program above *) (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 24 2017 *)

CROSSREFS

Sequence in context: A214235 A112550 A114927 * A297056 A292070 A297230

Adjacent sequences:  A286912 A286913 A286914 * A286916 A286917 A286918

KEYWORD

nonn

AUTHOR

Harvey P. Dale, May 24 2017

STATUS

approved

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Last modified October 13 20:38 EDT 2019. Contains 327981 sequences. (Running on oeis4.)