The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A260208 Least prime p such that 2p*n+1 = prime(q*n) for some prime q. 1
 2, 3, 2, 107, 271, 3, 3, 523, 17, 191, 73, 2707, 587, 2017, 19, 233, 57193, 7583, 9791, 7, 2111, 1373, 43, 109, 1283, 463, 8179, 25583, 7489, 1733, 9011, 7753, 7853, 887, 10141, 71, 1373, 7927, 509, 1433, 4513, 2399, 4211, 26407, 307, 2843, 58579, 3121, 5519, 38371 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjecture: a(n) exists for any n > 0. In general, if a > 0 is even and b is 1 or -1, then for any positive integer n there are primes p and q such that a*p*n+b = prime(q*n). 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..1000 Zhi-Wei Sun, Problems on combinatorial properties of primes, arXiv:1402.6641 [math.NT], 2014. EXAMPLE a(5) = 271 since 2*271*5+1 = 2711 = prime(79*5) with 271 and 79 both prime. MATHEMATICA PQ[n_, p_]:=PrimeQ[p]&&PrimeQ[PrimePi[p]/n] Do[k=0; Label[aa]; k=k+1; If[PQ[n, 2*Prime[k]*n+1]], Goto[bb], Goto[aa]]; Label[bb]; Print[n, " ", Prime[k]]; Continue, {n, 1, 50}] CROSSREFS Cf. A000040, A260197. Sequence in context: A075121 A075108 A265590 * A242457 A340261 A190146 Adjacent sequences:  A260205 A260206 A260207 * A260209 A260210 A260211 KEYWORD nonn AUTHOR Zhi-Wei Sun, Jul 19 2015 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 August 15 08:46 EDT 2022. Contains 356135 sequences. (Running on oeis4.)