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Primes p such that p + 4 is prime and p == 9 (mod 10).
18

%I #32 Sep 04 2022 18:52:14

%S 19,79,109,229,349,379,439,499,739,769,859,1009,1279,1429,1489,1549,

%T 1579,1609,1999,2239,2269,2389,2539,2659,2689,2749,3019,3079,3319,

%U 3529,3919,4129,4519,4639,4729,4789,4969,4999,5479,5569,5689,5779,5839,6199

%N Primes p such that p + 4 is prime and p == 9 (mod 10).

%C From _RĂ©mi Eismann_, May 14 2006; May 04 2007: (Start)

%C Also primes for which k is equal to 5 in A117078. Examples: prime(9) = prime(8) + (prime(8) mod 5) = 19 + (19 mod 5)=23; prime(23) = prime(22) + (prime(22) mod 5) = 79 + (79 mod 5)=83; prime(1359) = prime(1358) + (prime(1358) mod 5) = 11239+ (11239 mod 5)=11243.

%C The prime numbers in this sequence are of the form (10i-1) with i=(level(n)+1)/2, level(n) defined in A117563.

%C Consider A117078: a(n) = smallest k such that prime(n+1) = prime(n) + (prime(n) mod k), or 0 if no such k exists. Sequence gives values of prime(n) for which k=5. (End)

%C p is the lesser member of cousin primes (p,p+4) such that p == 9 (mod 10). - _Muniru A Asiru_, Jul 03 2017

%H Remi Eismann, <a href="/A074822/b074822.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CousinPrimes.html">Cousin Primes</a>

%t Prime[ Select[ Range[1000], Prime[ # ] + 4 == Prime[ # + 1] && Mod[ Prime[ # ], 10] == 9 & ]]

%t Transpose[Select[Partition[Prime[Range[820]],2,1],Last[#]-First[#] == 4 && Mod[ First[ #],10]==9&]][[1]] (* _Harvey P. Dale_, Oct 20 2011 *)

%o (PARI) is(n)=n%30==19 && isprime(n+4) && isprime(n) \\ _Charles R Greathouse IV_, Jul 12 2017

%o (PARI) list(lim)=my(v=List(),p=19); forprime(q=23,lim+4, if(q-p==4 && p%30==19, listput(v,p)); p=q); Vec(v) \\ _Charles R Greathouse IV_, Jul 12 2017

%Y Cf. A001223, A117078, A117563.

%Y Intersection of A023200 and A030433.

%K nonn,easy

%O 1,1

%A _Roger L. Bagula_, Sep 30 2002

%E Edited by _Robert G. Wilson v_ and _N. J. A. Sloane_, Oct 03 2002

%E Entry revised by _N. J. A. Sloane_, Feb 24 2007