A074822 Primes p such that p + 4 is prime and p == 9 (mod 10).

19, 79, 109, 229, 349, 379, 439, 499, 739, 769, 859, 1009, 1279, 1429, 1489, 1549, 1579, 1609, 1999, 2239, 2269, 2389, 2539, 2659, 2689, 2749, 3019, 3079, 3319, 3529, 3919, 4129, 4519, 4639, 4729, 4789, 4969, 4999, 5479, 5569, 5689, 5779, 5839, 6199

Offset: 1

Author

Roger L. Bagula, Sep 30 2002

Keywords

• nonn
• easy

Comments

From Rémi Eismann, May 14 2006; May 04 2007: (Start)

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.

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

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)

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

Links

• Remi Eismann, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Cousin Primes

Crossrefs

Cf. A001223, A117078, A117563.

Intersection of A023200 and A030433.

Programs

Mathematica

Prime[ Select[ Range[1000], Prime[ # ] + 4 == Prime[ # + 1] && Mod[ Prime[ # ], 10] == 9 & ]]
Transpose[Select[Partition[Prime[Range[820]],2,1],Last[#]-First[#] == 4 && Mod[ First[ #],10]==9&]][[1]] (* Harvey P. Dale, Oct 20 2011 *)

PARI

is(n)=n%30==19 && isprime(n+4) && isprime(n) \\ Charles R Greathouse IV, Jul 12 2017

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

Extensions

Edited by Robert G. Wilson v and N. J. A. Sloane, Oct 03 2002

Entry revised by N. J. A. Sloane, Feb 24 2007