

A152926


Numbers n with property that 19n+{2,4, 8,10} are two pairs of consecutive twin primes.


0



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 B. Jubin and F. Firoozbakht (SeqFan list, Dec 15 2008), they are == 21 (mod 30), see also the PARI code. 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

Table of n, a(n) for n=1..33.


EXAMPLE

19*171+{2,4}={3251,3253} and 19*171+{8,10}={3257,3259} are 85th and 86th twin primes.
19*3801+{2,4}={72221,72223} and 19*3801+{8,10}={72227,72229} are 935th and 936th twin primes.


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 *)


PROG

(PARI) /* The following prints the values of n (mod 30) such that 19n+{2, 4, 8, 10} are coprime with 30 and thus may be prime: It only prints 21. */ S=[2, 4, 8, 10]; for(n=1, 30, for(i=1, #S, gcd( 19*n+S[i], 30) >1 && next(2)); print(n)) \\ M. F. Hasler, Dec 24 2008


CROSSREFS

Cf. A001359.
Cf. A007530. [From 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



