A193423 Primes of the form x^2+y^3 with x, y and y^3 - x^2 >= 0.
2, 31, 43, 73, 89, 113, 241, 337, 347, 359, 379, 443, 487, 521, 593, 599, 733, 829, 953, 1009, 1049, 1129, 1213, 1289, 1361, 1367, 1753, 1777, 1907, 2017, 2089, 2213, 2297, 2341, 2393, 2521, 2689, 2753, 2953, 2969, 3221, 3391, 3571, 3631, 3797, 3833, 4051, 4133, 4159, 4177, 4217, 4457, 4721, 4937, 5237, 5813
Offset: 1
Keywords
Examples
2 is in the sequence because 2 is prime, 2=1^2+1^3 and 1^3-1^2=0; 31 is in the sequence because 31 is prime, 31=2^2+3^3 and 3^3-2^2>0; 43 is in the sequence because 43 is prime, 43=4^2+3^3 and 3^3-4^2>0;
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
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PARI
list(lim)=my(v=List(),t,B); lim\=1; for(b=1,sqrtn(lim+.5,3),B=b^3; for(a=1,min(lim-B,sqrtint(B)),if(isprime(t=B+a^2),listput(v,t)))); vecsort(Vec(v),,8) \\ Charles R Greathouse IV, Aug 28 2011
Extensions
Corrected by D. S. McNeil, Aug 27 2011
Comments