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A292788 For n > 1, a(n) = least positive k, not a power of n, such that the digital sum of k in base n equals the digital sum of k^3 in base n. 3
56953, 13, 2, 3, 20, 2, 6, 3, 8, 5, 1110, 3, 65, 8, 4, 7, 86, 9, 2374, 4, 8, 12, 114, 3, 99, 12, 135, 15, 3567, 4, 185, 15, 11, 16, 6, 19, 73, 20, 12, 5, 81, 6, 85, 23, 19, 24, 93, 7, 97, 24, 18, 27, 796, 28, 44, 7, 19, 28, 413, 4, 365, 32, 8, 31, 26, 21, 200 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

The term a(10) = 8 belongs to A070276.

For any n > 1, a(n^2) <= n.

Is this sequence defined for any n > 1 ?

Apparently, a(k) < k for any odd k > 3.

Among the first 99 999 terms, the digital sum of a(n) in base n is > n for n = 2, 12, 20, 30.

The scatterplot of the sequence shows beams on the upper part, which correspond to clusters of close points for which a(n) = k*n + (n-k-e) for some k > 0 and e in { 0, 2 }.

See also A292787 for a similar sequence involving squares instead of cubes.

The least positive k, not a power of 2, such that the hamming weight of k equals the hamming weight of k^4 is 34225258495.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 2..10000

Rémy Sigrist, Colorized scatterplot of the sequence for n=2..100000

EXAMPLE

For n = 3:

- let d_3 denote the digital sum in base 3 (d_3 = A053735),

- 1 is a power of 3,

- d_3(2) = 2 and d_3(2^3) = 4,

- 3 is a power of 3,

- d_3(4) = 2 and d_3(4^3) = 4,

- d_3(5) = 3 and d_3(5^3) = 7,

- d_3(6) = 2 and d_3(6^3) = 4,

- d_3(7) = 3 and d_3(7^3) = 5,

- d_3(8) = 4 and d_3(8^3) = 8,

- 9 is a power of 3,

- d_3(10) = 2 and d_3(10^3) = 4,

- d_3(11) = 3 and d_3(11^3) = 9,

- d_3(12) = 2 and d_3(12^3) = 4,

- d_3(13) = 3 and d_3(13^3) = 3,

- hence a(3) = 13.

MATHEMATICA

With[{kk = 10^5}, Table[SelectFirst[Complement[Range[2, kk], n^Range@ Floor@ Log[n, kk]], Total@ IntegerDigits[#, n] == Total@ IntegerDigits[#^3, n] &] /. k_ /; MissingQ@ k -> -1, {n, 2, 68}]] (* Michael De Vlieger, Sep 24 2017 *)

PROG

(PARI) a(n) = my (p=1); for (k=1, oo, if (k==p, p*=n, if (sumdigits(k, n) == sumdigits(k^3, n), return (k))))

CROSSREFS

Cf. A053735, A070276, A292787.

Sequence in context: A202568 A145685 A333951 * A138597 A206758 A019290

Adjacent sequences:  A292785 A292786 A292787 * A292789 A292790 A292791

KEYWORD

nonn,base,look

AUTHOR

Rémy Sigrist, Sep 23 2017

STATUS

approved

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Last modified August 5 06:37 EDT 2021. Contains 346458 sequences. (Running on oeis4.)