a(6)=7 because when the prime 29 is subtracted from the square 36, the result is another prime, 7

PROG

(UBASIC) 10 'sq less pr are prime 20 N=1:O=1:C=1 30 A=3:S=sqrt(N) 40 B=N\A 50 if B*A=N then 120 60 A=A+2 70 if A<=S then 40 80 R=O^2:Q=R-N 90 if N<R and N=prmdiv(N) and Q=prmdiv(Q) then print R; N; Q:N=N+2:C=C+1:goto 30 100 if C>31 then stop 120 N=N+2:if N<R then 30:else O=O+1:goto 80