A261533 Primes p such that p+2 is prime with prime(p+2)-prime(p)=6.
3, 5, 59, 2789, 5231, 6947, 8087, 11717, 15269, 16229, 17207, 17909, 18059, 18131, 24917, 28751, 35279, 37307, 39227, 39239, 41201, 43787, 45821, 47741, 51869, 53087, 53609, 58439, 64577, 69857, 70919, 75707, 79631, 84869, 92381, 93479, 96179, 102197, 102929, 106187
Offset: 1
Keywords
Examples
a(1) = 3 since 3 and 3+2 = 5 are twin prime, and prime(5)-prime(3) = 11-5 = 6. a(2) = 5 since 5 and 5+2 = 7 are twin prime, and prime(7)-prime(5) = 17-11 = 6.
References
- Zhi-Wei Sun, Problems on combinatorial properties of primes, in: M. Kaneko, S. Kanemitsu and J. Liu (eds.), Number Theory: Plowing and Starring through High Wave Forms, Proc. 7th China-Japan Seminar (Fukuoka, Oct. 28 - Nov. 1, 2013), Ser. Number Theory Appl., Vol. 11, World Sci., Singapore, 2015, pp. 169-187.
Links
- Zhi-Wei Sun, Table of n, a(n) for n = 1..2000
- Zhi-Wei Sun, Problems on combinatorial properties of primes, arXiv:1402.6641 [math.NT], 2014.
Programs
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Mathematica
f[n_]:=Prime[n] PQ[k_]:=PrimeQ[f[k]+2]&&f[f[k]+2]-f[f[k]]==6 n=0;Do[If[PQ[k],n=n+1;Print[n," ",f[k]]],{k,1,10119}] Select[Partition[Prime[Range[11000]],2,1],#[[2]]-#[[1]]==2&&Prime[#[[1]]+ 2]- Prime[#[[1]]]==6&][[All,1]] (* Harvey P. Dale, Apr 26 2020 *) -
PARI
isok(i)=p=prime(i);isprime(p+2)&&prime(p+2)-prime(p)==6; first(m)=my(v=vector(m));i=1;for(j=1,m,while(!isok(i),i++);v[j]=prime(i);i++);v; \\ Anders Hellström, Aug 23 2015
Comments