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.
As can be gathered from A127913, the first four records are A127913(1) = 3, A127913(6) = 6, A127913(7) = 7, A127913(10) = 9. Hence a(1) to a(4) are 3, 6, 7, 9.
The sixth record in A127913 is A129414(6) = 11 = A127913(22), hence a(6) = 22.
n=0: A001597(2) = 4 = 2^2 is the least perfect power q such that 0+q is an even semiprime; 0+4 = 4 = 2*2, hence a(0) = 2. n=11: A001597(7) = 27 = 3^3 is the least perfect power q such that 11+q is an even semiprime; 11+27 = 38 = 2*19, hence a(11) = 3. n=14: A001597(3) = 8 = 2^3 is the least perfect power q such that 14+q is an even semiprime; 14+8 = 22 = 2*11, hence a(14) = 2. n=27: A001597(1722) = 2476099 = 19^5 is the least perfect power q such that 27+q is an even semiprime; 27+2476099 = 2476126 = 2*1238063 and 1238063 is prime, hence a(27) = 19.
PP:=[1] cat [ n: n in [2..2500000] | IsPower(n) ]; prootesp:=function(n); if exists(k) {x: x in PP | IsEven(n+x) and IsPrime((n+x) div 2) } then y:=k; else return -1; end if; if y eq 1 then return 1; end if; _, b:=IsPower(y); return b; end function; [ prootesp(n): n in [0..100] ];
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