A142346 Primes of the form (p(n)+r(n))/2, where p(n)=n-th prime and r(n)=n-th nonprime.

2, 11, 47, 73, 131, 151, 173, 181, 227, 239, 271, 307, 367, 379, 383, 461, 523, 643, 661, 677, 743, 797, 991, 997, 1021, 1063, 1091, 1307, 1459, 1567, 1637, 1723, 1811, 1831, 1951, 1987, 1999, 2027, 2111, 2251, 2273, 2297, 2543, 2609, 2647, 2699, 2707, 2801

Offset

1,1

Links

Table of n, a(n) for n=1..48.

Example

If n=2, then (p(2)+r(2))/2=(3+1)/2=2=a(1).
If n=6, then (p(6)+r(6))/2=(13+9)/2=11=a(2).
If n=19, then (p(19)+r(19))/2=(67+27)/2=47=a(3).
If n=28, then (p(28)+r(28))/2=(107+39)/2=73=a(4).
If n=46, then (p(46)+r(46))/2=(199+63)/2=131=a(5), etc.

Maple

A141468 := proc(n) option remember ; if n = 1 then 0; else for a from procname(n-1)+1 do if not isprime(a) then RETURN(a) ; fi; od: fi: end: A000040 := proc(n) ithprime(n) ; end: for n from 1 to 3000 do c := A000040(n)+A141468(n) ; if c mod 2 = 0 then if isprime(c/2) then printf("%d, ", c/2) ; fi; fi; od: # R. J. Mathar, Nov 03 2008

Mathematica

Module[{nn=1000, np, len}, np=Select[Range[0, nn], !PrimeQ[#]&]; len= Length[ np]; Select[Total/@Thread[{np, Prime[Range[len]]}]/2, PrimeQ]] (* Harvey P. Dale, Jul 08 2020 *)

Crossrefs

Cf. A000040, A141468.

Sequence in context: A292533 A140305 A229019 * A106980 A089682 A211671

Adjacent sequences: A142343 A142344 A142345 * A142347 A142348 A142349

Keyword

nonn

Author

Juri-Stepan Gerasimov, Sep 19 2008

Extensions

239 inserted, 367 inserted and extended by R. J. Mathar, Nov 03 2008

Status

approved