

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
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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]] (* JeanFrançois Alcover, Feb 25 2015 *)
Select[Range[6, 243000, 15], AllTrue[19#+{2, 4, 8, 10}, PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 09 2020 *)


CROSSREFS

Cf. A001359.
Cf. A007530.  M. F. Hasler, Dec 24 2008
Sequence in context: A195279 A016058 A332418 * A239270 A262142 A206595
Adjacent sequences: A152923 A152924 A152925 * A152927 A152928 A152929


KEYWORD

nonn


AUTHOR

Zak Seidov, Dec 15 2008


STATUS

approved



