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A074822
Primes p such that p + 4 is prime and p == 9 (mod 10).
18
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
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
Intersection of A023200 and A030433.
Sequence in context: A350194 A372757 A132234 * A139871 A142789 A158491
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