

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
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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

N. J. A. Sloane


STATUS

approved



