A130467 Primes p of the form p=a^2+b^3, such that q =A130468(n)= a^3+b^2 is prime and greater than p; p < q ; b < a.
17, 43, 89, 113, 127, 223, 233, 269, 337, 443, 449, 487, 811, 919, 1129, 1213, 1361, 1471, 2089, 2089, 2521, 2647, 2731, 2953, 2969, 3041, 3259, 3391, 3433, 4093, 4441, 4651, 4721, 4721, 4969, 5237, 5309, 5527, 5689, 6121, 6329, 6361, 6427, 7057, 7121
Offset: 1
Examples
a(1)=17 because 17=3^2+2^3=9+8 and A130468(1)= 31=3^3+2^2=27+4; 17<31 ; 2 < 3; a(5)=127 because 127=10 ^2 + 3 ^3= 100+27 and A130468(5)= 1009 = 10 ^3 + 3 ^2 = 1000+9; 127< 1009; 3 < 10
Programs
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Mathematica
pgpQ[{b_,a_}]:=Module[{p1=a^2+b^3,p2=b^2+a^3},AllTrue[{p1,p2},PrimeQ] && p1
Formula
p=a^2+b^3;q=a^3+b^2