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

1,2

Links

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

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

Crossrefs

Cf. A075593, A075594, A103824.

Sequence in context: A131896 A114380 A293130 * A073238 A010655 A123596

Adjacent sequences: A103822 A103823 A103824 * A103826 A103827 A103828

Keyword

nonn

Author

Ray Chandler Feb 16 2005

Extensions

Definition corrected by Zak Seidov, Feb 20 2005

Status

approved