The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A238814 Primes p with prime(p) - p + 1 and prime(q) - q + 1 both prime, where q is the first prime after p. 3
 2, 3, 5, 13, 41, 83, 199, 211, 271, 277, 293, 307, 349, 661, 709, 743, 751, 823, 907, 1117, 1447, 1451, 1741, 1747, 2203, 2371, 2803, 2819, 2861, 2971, 3011, 3251, 3299, 3329, 3331, 3691, 3877, 4021, 4027, 4049, 4051, 4093, 4129, 4157, 4447, 4513, 4549, 4561, 4751, 4801, 5179, 5479, 5519, 5657, 5813, 6007, 6011, 6571, 7057, 7129 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjecture: The sequence is infinite, in other words, A234695 contains infinitely many consecutive prime pairs prime(k) and prime(k+1). This is motivated by the comments in A238766 and A238776, and the sequence is a subsequence of A234695. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..10000 Zhi-Wei Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014. EXAMPLE a(1) = 2 since prime(2) - 2 + 1 = 3 - 1 = 2 and prime(3) - 3 + 1 = 5 - 2 = 3 are both prime. a(2) = 3 since prime(3) - 3 + 1 = 5 - 2 = 3 and prime(5) - 5 + 1 = 11 - 4 = 7 are both prime. MATHEMATICA p[k_]:=PrimeQ[Prime[Prime[k]]-Prime[k]+1] n=0 Do[If[p[k]&&p[k+1], n=n+1; Print[n, " ", Prime[k]]], {k, 1, 914}] Select[Prime[Range[1000]], AllTrue[{Prime[#]-#+1, Prime[NextPrime[#]]-NextPrime[ #]+1}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 24 2019 *) PROG (PARI) step(p, k)=k++; while(k--, p=nextprime(p+1)); p p=0; forprime(r=2, 1e6, if(isprime(p++) && isprime(r-p+1), q=nextprime(p+1); if(isprime(step(r, q-p)-q+1), print1(p", ")))) \\ Charles R Greathouse IV, Mar 06 2014 CROSSREFS Cf. A000040, A234694, A234695, A238766, A238776. Sequence in context: A087362 A038560 A240838 * A000756 A192241 A093999 Adjacent sequences: A238811 A238812 A238813 * A238815 A238816 A238817 KEYWORD nonn AUTHOR Zhi-Wei Sun, Mar 05 2014 STATUS approved

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

Last modified June 18 04:26 EDT 2024. Contains 373468 sequences. (Running on oeis4.)