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A111103
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a(1) = 1; for n > 1: a(n) = smallest cube > a(n-1) such that a(n) - a(n-1) = m*p for some m and a prime p that is not smaller than the primes used previously; in case there is more than one p take the largest.
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1
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1, 8, 27, 64, 125, 343, 729, 1000, 1331, 1728, 6859, 9261, 12167, 13824, 15625, 17576, 79507, 103823, 132651, 166375, 175616, 226981, 357911, 421875, 493039, 571787, 614125, 658503, 753571, 778688, 1092727, 1331000, 1860867, 1906624, 2248091
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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EXAMPLE
| 8 = 1+7; 27 = 8+19; 64 = 27+37; 125 = 64+61; 343 = 125+2*109; 729 = 343+2*193.
216 = 6^3 is not in the sequence, since 216-125 = 91 = 7*13 and 13 is smaller than the previously used prime 37.
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PROG
| (PARI) {q=1; print1(a=1, ", "); for(n=2, 140, c=n^3; f=factor(c-a); if((p=f[matsize(f)[1], 1])>=q, print1(c, ", "); q=p; a=c))}
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CROSSREFS
| See A111131 for another version.
Sequence in context: A125496 A030289 A111131 * A076969 A179163 A050462
Adjacent sequences: A111100 A111101 A111102 * A111104 A111105 A111106
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KEYWORD
| nonn
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AUTHOR
| Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), Oct 14 2005
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EXTENSIONS
| Edited, corrected and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 16 2005
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