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Search: id:A054221
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| A054221 |
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Consider all integer triples (i,j,k), j,k>0, with binomial(i+2,3)=binomial(j+2,3)+k^3, ordered by increasing i; sequence gives i values. |
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4
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| 7, 8, 10, 23, 27, 48, 64, 125, 199, 216, 343, 512, 621, 729, 978, 1000, 1222, 1331, 1728, 2197, 2744, 3375, 3563, 4034, 4096, 4331, 4913, 5017, 5832, 6442, 6859, 6886, 7783, 8000, 8699, 9261, 10648, 11157, 12167, 12287, 12386, 13824, 15625, 17576, 19683
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Sequence contains all positive cubes, since binomial(n+2,3)-binomial(n,3)=n^2. j values are A054222 and k values are A054223.
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EXAMPLE
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binomial(7+2,3)=84=binomial(4+2,3)+4^3; binomial(8+2,3)=120=binomial(6+2,3)+4^3;
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PROGRAM
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(C) #include <stdio.h> #include <limits.h> #include <math.h> unsigned A000578inv(unsigned long long n) { unsigned long long n3 = (unsigned long long)cbrt((double)n) ; for(unsigned long long k= n3-1 ; k <= n3+1 ; k++) if ( k*k*k == n) return k ; return 0 ; } int main(int argc, char *argv[]) { const unsigned long long imax = cbrt((double)ULLONG_MAX)-2. ; for(unsigned i=1; i<imax; i++) { unsigned long long i3 = i*(unsigned long long)(i+1)*(unsigned long long)(i+2) ; for(unsigned j=1 ; j < i ; j++) { unsigned long long k3 = i3- j*(unsigned long long)(j+1)*(unsigned long long)(j+2) ; if( k3 % 6 == 0) { unsigned k=A000578inv(k3/6) ; if ( k ) { printf("%d, ", i) ; fflush(stdout) ; } } } } } - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 10 2006
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CROSSREFS
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A054222, A054223.
Sequence in context: A127164 A111064 A071117 this_sequence A090385 A102963 A117619
Adjacent sequences: A054218 A054219 A054220 this_sequence A054222 A054223 A054224
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KEYWORD
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nice,nonn
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AUTHOR
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Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Feb 04 2000
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 10 2006
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