A158350 Primes p such that previousPrime(p) + p -+ 1 are twin primes.

7, 11, 17, 23, 31, 71, 101, 127, 233, 307, 311, 409, 419, 443, 617, 647, 661, 719, 743, 811, 839, 863, 941, 1049, 1061, 1361, 1487, 1667, 1697, 1889, 2003, 2053, 2129, 2131, 2243, 2267, 2551, 2647, 2711, 2753, 2767, 2833, 3049, 3109, 3163, 3229, 3299, 3331

Offset

1,1

Comments

Sum of two consecutive primes = arithmetic mean of twin primes.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Example

5+7=12-+1 primes, 7+11=18-+1 primes, 13+17-+1 primes, ...

Maple

t1:=[]; for n from 2 to 1000 do p:=ithprime(n); q:=prevprime(p);
if isprime(p+q-1) and isprime(p+q+1) then t1:=[op(t1), p]; fi; od: t1; # N. J. A. Sloane, Dec 24 2012

Mathematica

lst={}; Do[p0=Prime[n]; p1=Prime[n+1]; a=p0+p1; If[PrimeQ[a-1] && PrimeQ[a+1], AppendTo[lst, p1]], {n, 1000}]; lst
Select[Partition[Prime[Range[500]], 2, 1], AllTrue[Total[#]+{1, -1}, PrimeQ]&][[;; , 2]] (* Harvey P. Dale, May 31 2026 *)

Crossrefs

Cf. A099349.

Sequence in context: A092737 A072669 A108101 * A048203 A370009 A088176

Adjacent sequences: A158347 A158348 A158349 * A158351 A158352 A158353

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Mar 16 2009

Status

approved