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A152926 Numbers k with property that 19*k + {2,4,8,10} are two pairs of consecutive twin primes. 1
171, 3801, 5781, 8721, 8781, 17601, 18231, 19011, 24741, 28251, 40431, 48951, 49371, 58821, 70521, 79401, 79701, 83391, 87321, 95781, 96501, 99501, 102861, 109431, 123171, 125061, 137091, 177201, 220311, 224511, 225561, 229551, 242451 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All terms == 6 (mod 15).

These are numbers n such that 19n+2 is in A007530. As proved by Benoit Jubin and Farideh Firoozbakht (SeqFan list, Dec 15 2008), they are == 21 (mod 30). The same holds for p=19 replaced by p=7,11,13,17,23,29,31,... with residue class n=27,9,3,27,3,21,9,... (mod 30). - M. F. Hasler, Dec 24 2008

LINKS

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

Farideh Firoozbakht, all terms == 21 (mod 30), message on the SeqFan list, Dec 17 2008

EXAMPLE

171 is in the sequence because 19*171 + {2,4} = {3251,3253} and 19*171 + {8,10} = {3257,3259} are 85th and 86th twin primes.

3801 is in the sequence because 19*3801 + {2,4} = {72221,72223} and 19*3801 + {8,10} = {72227,72229} are 935th and 936th twin primes.

MAPLE

select(n -> andmap(t -> isprime(19*n+t), {2, 4, 8, 10}), [seq(i, i=21..10^6, 30)]); # Robert Israel, Mar 20 2018

MATHEMATICA

Reap[For[n = 21, n < 10^6, n = n + 30, nn = 19*n + {2, 4, 8, 10}; If[CoprimeQ @@ nn, If[And @@ PrimeQ /@ nn, Sow[n]]]]][[2, 1]] (* Jean-Fran├žois Alcover, Feb 25 2015 *)

CROSSREFS

Cf. A001359.

Cf. A007530. - M. F. Hasler, Dec 24 2008

Sequence in context: A185611 A195279 A016058 * A239270 A262142 A206595

Adjacent sequences:  A152923 A152924 A152925 * A152927 A152928 A152929

KEYWORD

nonn

AUTHOR

Zak Seidov, Dec 15 2008

STATUS

approved

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Last modified July 16 23:38 EDT 2018. Contains 312693 sequences. (Running on oeis4.)