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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. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..45.

FORMULA

p=a^2+b^3;q=a^3+b^2

EXAMPLE

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

MATHEMATICA

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 *)

CROSSREFS

Cf. A130468; A000040.

Sequence in context: A031340 A172044 A098072 * A112885 A093191 A033703

Adjacent sequences:  A130464 A130465 A130466 * A130468 A130469 A130470

KEYWORD

easy,nonn

AUTHOR

Tomas Xordan, May 27 2007

STATUS

approved

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Last modified September 30 18:12 EDT 2020. Contains 337440 sequences. (Running on oeis4.)