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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 Fröhlich, 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

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Last modified November 21 12:34 EST 2017. Contains 295001 sequences.