A111103 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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.