A248705 The cubes related to the strictly increasing subsequence of A053668(n), n >= 1.

1, 8, 27, 64, 343, 729, 2744, 3375, 6859, 35937, 46656, 148877, 287496, 438976, 778688, 2985984, 3869893, 8489664, 34645976, 43986977, 58863869, 75686967, 398688256, 426957777, 485587656, 596947688, 835896888, 1693669888, 2548895896, 2954987875, 4758586568

Offset

1,2

Comments

The triangular numbers of this form are at A246753.

The squares of this form are at A248648.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..139 (first 116 terms from K. D. Bajpai)

Example

a(4) = 64 = 4*4*4, which is a cube. Product of its digits = 6*4 = 24.
a(5) = 343 = 7*7*7, which is a cube. Product of its digits = 3*4*3 = 36.
Since 36 > 24, 64 and 343 appear in the sequence.
As suggested by Wolfdieter Lang, examples further clarified:
(Start)
A053668 is sieved (from left to right):
1, 2,  3,  4,   5,   6,   7,   8,   9, ....(numbers: k)
1, 8, 27, 64, 125, 216, 343, 512, 729, ....(cubes: k^3)
1, 8, 14, 24,  10,  12,  36,  10, 126, ....(prod of digits of k^3)
1, 8, 14, 24,   X,   X,  36,   X, 126, ....(sieved products)
and related leftover cubes are:
1, 8, 27, 64,           343,      729, ....(leftover cubes)
(End)

Mathematica

A248705 = {}; t = 0; Do[s = Apply[Times, IntegerDigits[n^3]]; If[s > t, t = s; AppendTo[A248705, n^3]], {n, 1, 10^4}]; A248705

Prog

(PARI) \\ For b-file
c = 0; k = 0; for(n=1, 5*10^8, d = digits(n^3); p = prod(i = 1, #d, d[i]); while(p > k, c++; print(c, "  ", n^3); k = p))
(Python)
from operator import mul
from functools import reduce
A248705_list, x, m  = [], 0, [6, -6, 1, 0]
for _ in range(10**9):
    for i in range(3):
        m[i+1]+= m[i]
    xn = reduce(mul, [int(d) for d in str(m[-1])], 1)
    if xn > x:
        x = xn
        A248705_list.append(m[-1]) # Chai Wah Wu, Nov 19 2014

Crossrefs

Cf. A000578, A053668, A230041, A246569, A246753, A248648.

Sequence in context: A121652 A112989 A018832 * A030293 A030479 A061096

Adjacent sequences: A248702 A248703 A248704 * A248706 A248707 A248708

Keyword

nonn,base

Author

K. D. Bajpai, Oct 13 2014

Status

approved