A173970 Primes p such that 2*p-NextPrime are prime numbers.

5, 7, 23, 47, 53, 73, 157, 173, 211, 233, 257, 263, 353, 373, 563, 593, 607, 619, 647, 653, 733, 947, 977, 1069, 1097, 1103, 1123, 1187, 1223, 1283, 1367, 1433, 1453, 1459, 1493, 1499, 1511, 1613, 1709, 1747, 1753, 1759, 1789, 1889, 1907, 2099, 2161, 2287

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Mar 03 2010

Keywords

• nonn

Comments

2*5-7=3, 2*7-11=3, 2*23-29=17,..

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Programs

Magma

[p:p in PrimesUpTo(2500)| IsPrime(2*p-NextPrime(p))]; // Marius A. Burtea, Jul 03 2019

Maple

P:= select(isprime, [2,seq(i,i=1..10000,2)]):
Q:= 2*P[1..-2]-P[2..-1]:
P[select(t -> isprime(Q[t]),[$1..nops(Q)])]; # Robert Israel, Jul 03 2019

Mathematica

lst={};Do[p=Prime[n];If[PrimeQ[2*p-Prime[n+1]],AppendTo[lst,p]],{n,6!}];lst
Select[Prime[Range[400]],PrimeQ[2#-NextPrime[#]]&] (* Harvey P. Dale, May 04 2021 *)