A103825 Choose a(n) to be the smallest number not yet used such that: a(1) = 1, a(2n) = composite, a(2n+1) = prime and partial sums are alternately prime or composite.

1, 4, 3, 9, 5, 15, 2, 8, 7, 25, 11, 49, 13, 21, 17, 33, 19, 27, 23, 39, 29, 119, 31, 77, 37, 35, 41, 51, 43, 45, 47, 55, 53, 57, 59, 91, 61, 65, 67, 87, 71, 69, 73, 93, 79, 85, 83, 95, 89, 63, 97, 81, 101, 99, 103, 75, 107, 105, 109, 141, 113, 115, 127, 125, 131, 111, 137

Offset: 1

Author

Ray Chandler Feb 16 2005

Keywords

• nonn

Links

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

Crossrefs

Cf. A075593, A075594, A103824.

Programs

Maple

N:= 1000: # for terms before the first term > N
Avail:= [$2..N]:
A[1]:= 1: T:= 1:
for n from 2 while assigned(A[n-1]) do
  for j from 1 to N+1-n do
    x:= Avail[j];
    if (n::even and isprime(x+T) and not isprime(x)) or
       (n::odd and isprime(x) and not isprime(x+T)) then
      A[n]:= x; T:= T+x;
      Avail:= subsop(j=NULL, Avail);
      break
    fi
  od
od:
seq(A[i],i=1..n-2); # Robert Israel, Nov 26 2020

Extensions

Definition corrected by Zak Seidov, Feb 20 2005