A280028 a(1)=1; thereafter, if n even, a(n) = a(n-1)-st prime, and if n odd, a(n) = a(n-1)-st nonprime.

1, 2, 4, 7, 12, 37, 52, 239, 301, 1993, 2338, 20753, 23356, 266587, 291968, 4134187, 4446630, 75947059, 80652283, 1625456353, 1710094788, 39954587527, 41737658509, 1114336791787, 1157634258442, 34900173534517, 36096139358620, 1216553712004063

Offset: 1

Author

N. J. A. Sloane, Dec 25 2016

Keywords

• nonn

Comments

This is the sequence S_1 mentioned in A141436. The primes and nonprimes alternate.

Crossrefs

Cf. A000040, A018252, A141436, A280029, A280030.

Programs

Maple

P:=n->ithprime(n);
# let b1 be a list of the nonprimes (from the b-file for A018252)
N:=n->if n<=nops(b1) then b1[n] else 0; fi;;
f:=proc(m) local S,n,sw,t; global P,N;
S:=[m]; t:=m;
   if isprime(m) then sw:=1; else sw:=2; fi;
if sw=1 then
   for n from 2 to 60 do
   if n mod 2 = 0 then t:=N(t); if t=0 then return(S); fi; else t:=P(t); fi; S:=[op(S),t];
   od:
else
   for n from 2 to 60 do
   if n mod 2 = 0 then t:=P(t); else t:=N(t); if t=0 then return(S); fi; fi; S:=[op(S),t];
   od:
fi;
S;
end;
f(1); # A280028
f(3); # A280029
f(5); # A280030

Mathematica

nonPrime[n_Integer] := FixedPoint[n + PrimePi@# &, n + PrimePi@ n]; a[n_] := If[ OddQ@ n, nonPrime[ a[n -1]], Prime@a[n -1]]; a[1] = 1; Array[a, 26] (* Robert G. Wilson v, Dec 28 2016 *)

Extensions

a(13)-a(27) from Hans Havermann, Dec 25 2016

a(28) from Chai Wah Wu, Dec 26 2016