This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
p=3; s={p}; Do[q=Prime[n]; If[PrimeQ[(p+q)/4], AppendTo[s,q]; p=q], {n, 3, 1000}]; s
nxt[n_]:=Module[{p=NextPrime[n]},While[!PrimeQ[(n+p)/4],p=NextPrime[ p]]; p]; NestList[nxt,3,50] (* Harvey P. Dale, Nov 25 2013 *)
a(4) = 21 because a(3) = 10, 21 = 3 * 7 is a semiprime > 10, 10 + 21 = 31 is prime, and no smaller semiprime > 10 works.
R:= 4: s:= 4:
for count from 2 to 100 do
for t from s+1 by 2 do
if isprime(s+t) and numtheory:-bigomega(t) = 2 then
R:= R,t; s:= t; break
fi
od
od:
R;
s = {q = 4}; Do[p = q + 1; While[ PrimeOmega[p] != 2, p = p + 2]; AppendTo[s, q = p], {120}]; s
Table[((2*n +1)*(2*n^2 + 2*n -1)+ 5*(-1)^n)/4,{n,83}]
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