This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A029710 Primes such that next prime is 4 greater. 27
 7, 13, 19, 37, 43, 67, 79, 97, 103, 109, 127, 163, 193, 223, 229, 277, 307, 313, 349, 379, 397, 439, 457, 463, 487, 499, 613, 643, 673, 739, 757, 769, 823, 853, 859, 877, 883, 907, 937, 967, 1009, 1087, 1093, 1213, 1279, 1297, 1303, 1423, 1429 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Union with A124588 gives A124589. - Reinhard Zumkeller, Dec 23 2006 For any prime p > 3, if p + 4 is prime then necessarily it is the next prime. But there cannot be three consecutive primes with mutual distance 4: If p and p + 4 are prime, then p+8 is an odd multiple of 3 (cf. formula). - M. F. Hasler, Jan 15 2013 The smaller members p of cousin prime pairs (p,p+4) excluding p=3. - Marc Morgenegg, Apr 19 2016 LINKS R. Zumkeller, Table of n, a(n) for n = 1..1000 FORMULA a(n) = A031505(n + 1) - 4 = A029708(n) - 2. a(n) = 1 (mod 6) for all n; (a(n) + 2)/3 = A157834(n), i.e., a(n) = 3*A157834(n) - 2. - M. F. Hasler, Jan 15 2013 EXAMPLE 79 is a term as the next prime is 79 + 4 = 83. 3 is not a term even though 3 + 4 = 7 is prime, since it is not the next one. MAPLE for i from 1 to 226 do if ithprime(i+1) = ithprime(i) + 4 then print({ithprime(i)}); fi; od; # Zerinvary Lajos, Mar 19 2007 MATHEMATICA Select[Prime[Range[225]], NextPrime[#] == # + 4 &] (* Alonso del Arte, Jan 17 2013 *) Transpose[Select[Partition[Prime[Range[300]], 2, 1], #[[2]]-#[[1]]==4&]] [[1]] (* Harvey P. Dale, Mar 28 2016 *) PROG (PARI) forprime(p=1, 1e4, if(nextprime(p+1)-p==4, print1(p, ", "))) \\ Felix FrÃ¶hlich, Aug 16 2014 CROSSREFS Essentially the same as A023200. Cf. A001359, A029708, A031505, A124588, A124589, A157834. Sequence in context: A152087 A098059 A078860 * A145897 A078863 A263091 Adjacent sequences:  A029707 A029708 A029709 * A029711 A029712 A029713 KEYWORD nonn AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.