cp's OEIS Frontend

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.

%I A103825 #8 Nov 26 2020 19:23:36
%S A103825 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,
%T A103825 35,41,51,43,45,47,55,53,57,59,91,61,65,67,87,71,69,73,93,79,85,83,95,
%U A103825 89,63,97,81,101,99,103,75,107,105,109,141,113,115,127,125,131,111,137
%N 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.
%H A103825 Robert Israel, <a href="/A103825/b103825.txt">Table of n, a(n) for n = 1..10000</a>
%p A103825 N:= 1000: # for terms before the first term > N
%p A103825 Avail:= [$2..N]:
%p A103825 A[1]:= 1: T:= 1:
%p A103825 for n from 2 while assigned(A[n-1]) do
%p A103825   for j from 1 to N+1-n do
%p A103825     x:= Avail[j];
%p A103825     if (n::even and isprime(x+T) and not isprime(x)) or
%p A103825        (n::odd and isprime(x) and not isprime(x+T)) then
%p A103825       A[n]:= x; T:= T+x;
%p A103825       Avail:= subsop(j=NULL, Avail);
%p A103825       break
%p A103825     fi
%p A103825   od
%p A103825 od:
%p A103825 seq(A[i],i=1..n-2); # _Robert Israel_, Nov 26 2020
%Y A103825 Cf. A075593, A075594, A103824.
%K A103825 nonn
%O A103825 1,2
%A A103825 _Ray Chandler_ Feb 16 2005
%E A103825 Definition corrected by _Zak Seidov_, Feb 20 2005