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

1,1

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

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 *)

Prog

(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

Crossrefs

Cf. A001223, A117078, A117563.

Intersection of A023200 and A030433.

Sequence in context: A213832 A350194 A132234 * A139871 A142789 A158491

Adjacent sequences: A074819 A074820 A074821 * A074823 A074824 A074825

Keyword

nonn,easy

Author

Roger L. Bagula, Sep 30 2002

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

Status

approved