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A074822
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Primes p such that p + 4 is prime and p == 9 (mod 10).
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18
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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Remi Eismann, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Cousin Primes
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A001223, A117078, A117563.
Intersection of A023200 and A030433.
Sequence in context: A041700 A213832 A132234 * A139871 A142789 A158491
Adjacent sequences: A074819 A074820 A074821 * A074823 A074824 A074825
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KEYWORD
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nonn,easy
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AUTHOR
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Roger L. Bagula, Sep 30 2002
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EXTENSIONS
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Edited by Robert G. Wilson v and N. J. A. Sloane, Oct 03 2002
Entry revised by N. J. A. Sloane, Feb 24 2007
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STATUS
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approved
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