A111103 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.

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

Offset

1,2

Links

Table of n, a(n) for n=1..35.

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.

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))}

Crossrefs

See A111131 for another version.

Sequence in context: A125496 A030289 A111131 * A076969 A179163 A050462

Adjacent sequences: A111100 A111101 A111102 * A111104 A111105 A111106

Keyword

nonn

Author

Giovanni Teofilatto, Oct 14 2005

Extensions

Edited, corrected and extended by Klaus Brockhaus, Oct 16 2005

Status

approved