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%I #5 Jul 30 2018 17:30:16
%S 17,43,89,113,127,223,233,269,337,443,449,487,811,919,1129,1213,1361,
%T 1471,2089,2089,2521,2647,2731,2953,2969,3041,3259,3391,3433,4093,
%U 4441,4651,4721,4721,4969,5237,5309,5527,5689,6121,6329,6361,6427,7057,7121
%N 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.
%F p=a^2+b^3;q=a^3+b^2
%e 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;
%e 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
%t pgpQ[{b_,a_}]:=Module[{p1=a^2+b^3,p2=b^2+a^3},AllTrue[{p1,p2},PrimeQ] && p1<p2]; Take[#[[2]]^2+#[[1]]^3&/@Select[Subsets[Range[100],{2}],pgpQ]//Sort,50] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Jul 30 2018 *)
%Y Cf. A130468; A000040.
%K easy,nonn
%O 1,1
%A _Tomas Xordan_, May 27 2007
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