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A099808 If a,b are primes which satisfy the Diophantine equation a^3 + b^3 = c^2, then this sequence consists of the numbers sqrt((a+b)/48), sorted by the magnitude of c. 5
1, 15, 28, 35, 44, 44, 55, 56, 91, 90, 88, 119, 161, 165, 200, 184, 273, 319, 285, 357, 377, 400, 380, 434, 550, 517, 592, 615, 638, 667, 682, 666, 740, 697, 784, 688, 825, 682, 846, 770, 893, 814, 868, 925, 775, 899, 885, 1007, 1045, 1040, 1078, 1184, 1015 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For each n let a=A099806[n], b=A099807[n]. Then sqrt((a+b)/48) is an integer and equals A099808[n]. Note that a^3 + b^3 = c^2 factors as (a+b)*(a^2-a*b+b^2). The first factor (a+b) is 48*d^2, some d. This sequence tabulates the d values. Remember, a and b are prime numbers.

LINKS

Table of n, a(n) for n=0..52.

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

EXAMPLE

From 11^3 + 37^3 = 228^2 we get sqrt((a+b)/48)=(11+37)/48=1, so 1 is in the sequence.

CROSSREFS

Cf. A099806, A099807, A098970, A099809.

Sequence in context: A223449 A031334 A178958 * A291054 A134621 A106499

Adjacent sequences:  A099805 A099806 A099807 * A099809 A099810 A099811

KEYWORD

nonn

AUTHOR

James R. Buddenhagen, Oct 26 2004

EXTENSIONS

Example corrected by Harvey P. Dale, Apr 12 2011.

STATUS

approved

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Last modified September 26 01:55 EDT 2021. Contains 347664 sequences. (Running on oeis4.)