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A099809 Let a,b be prime numbers satisfying the Diophantine equation a^3+b^3=(a+b)*(a^2-a*b+b^2)=c^2. Then the second factor a^2-a*b+b^2 is 3*e^2 for some integer e. This sequence tabulates the 'e' values, sorted by magnitude of c. 4
19, 4513, 14689, 32401, 26929, 48019, 44641, 72739, 124099, 179683, 211249, 288979, 395089, 386131, 587233, 905059, 1040419, 1410049, 2237011, 1919779, 2078209, 2220451, 2950963, 2767489, 4919971, 5582449, 5019889, 5255761 (list; graph; refs; listen; history; text; internal format)



For each n let a=A099806[n], b=A099807[n], c/12=A098970. Then a^3+b^3=c^2. The left side factors as (a+b)*(a^2-a*b+b^2). The second factor is 3*e^2 for some integer e. The sequence tabluates the 'e' values. These 'e' values all have the form 3*M^4+N^4, for some pair M,N of relatively prime integers of opposite parity. Remember, a and b are prime numbers.


Table of n, a(n) for n=0..27.

James Buddenhagen, Two Primes Cubed which Sum to a Square.


11^3+37^3=228^2, 11^2-11*37+37^2=3*e^2 with e=19, so 19 is in the sequence.


Cf. A099806, A099807, A098970, A099808.

Sequence in context: A238563 A281820 A213450 * A271588 A233464 A145214

Adjacent sequences:  A099806 A099807 A099808 * A099810 A099811 A099812




James R. Buddenhagen, Oct 26 2004



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Last modified December 12 12:30 EST 2019. Contains 329958 sequences. (Running on oeis4.)