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Search: id:A038853
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| A038853 |
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Numbers that are divisible by 5 and are the difference between two (different positive) cubes in at least one way. |
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+0
2
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| 215, 335, 485, 665, 875, 1115, 1330, 1385, 1685, 1720, 2015, 2170, 2375, 2680, 2765, 3185, 3250, 3635, 3880, 4095, 4115, 4570, 4625, 4905, 5165, 5320, 5735, 5805, 6130, 6335, 6795, 6965, 7000, 7625, 7875, 7930, 8315, 8920, 9035, 9045, 9260, 9785, 9970
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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A number is in this sequence iff it is of the form (k+5j)^3-k^3, where k,j are any positive integers, since (k+d)^3 - k^3 = d(3(k+d/2)^2+d^2/4) = 0 (mod 5) iff d=0 (mod 5), since 3x^2 =-y^2/4 (mod 5) iff x=y=0 (mod 5). - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Jun 07 2007
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PROGRAM
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(PARI) A038853(Nmax=10^4, a=[]) = { local(t, j5); for(j=1, Nmax^(1/3)/5, j5=5*j; for(k=1, sqrt((Nmax/j5-j5^2-3*j5)/3), if(Nmax<t=(k+j5)^3-k^3, next); a=concat(a, t))); vecsort(a) } - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Jun 07 2007
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CROSSREFS
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Sequence in context: A092796 A076159 A046011 this_sequence A038860 A038867 A120536
Adjacent sequences: A038850 A038851 A038852 this_sequence A038854 A038855 A038856
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KEYWORD
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nonn
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AUTHOR
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Jeff Burch (gburch(AT)erols.com)
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EXTENSIONS
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Corrected by M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Jun 07 2007
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