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A246057 a(n) = (5*10^n - 2)/3. 9
1, 16, 166, 1666, 16666, 166666, 1666666, 16666666, 166666666, 1666666666, 16666666666, 166666666666, 1666666666666, 16666666666666, 166666666666666, 1666666666666666, 16666666666666666, 166666666666666666, 1666666666666666666, 16666666666666666666 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(k-1) = (10^k - 4)/6, together with b(k) = 3*a(k-1) + 2 = A093143(k) and c(k) = 2*a(k-1) + 1 = A002277(k) are k-digit numbers for k >= 1 satisfying the so-called curious cubic identity a(k-1)^3 + b(k)^3 + c(k)^3 = a(k)*10^(2*k) + b(k)*10^k + c(k) (concatenated a(k)b(k)c(k)). This k-family and the proof of the identity has been given in the introduction of the van der Poorten reference. Thanks go to S. Heinemeyer for bringing these identities to my attention. - Wolfdieter Lang, Feb 07 2017

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..100

A. van der Poorten, K. Thomsen, and M. Wiebe, A curious cubic identity and self-similar sums of squares, The Mathematical Intelligencer, v.29(2), pp. 39-41, March 2007.

Index entries for linear recurrences with constant coefficients, signature (11,-10).

FORMULA

G.f.: (1 + 5*x)/((1 - x)*(1 - 10*x)).

a(n) = 11*a(n-1) - 10*a(n-2).

EXAMPLE

Curious cubic identities (see a comment and reference above): 1^3 + 5^3 + 3^3 = 153, 16^3 + 50^3 + 33^3 = 165033, 166^3 + 500^3 + 333^3 = 166500333, ... - Wolfdieter Lang, Feb 07 2017

MATHEMATICA

Table[(5 10^n - 2)/3, {n, 0, 20}]

PROG

(MAGMA) [(5*10^n-2)/3: n in [0..20]];

(PARI) vector(50, n, (5*10^(n-1)-2)/3) \\ Derek Orr, Aug 13 2014

CROSSREFS

Cf. sequences with terms of the form 1k..k where the digit k is repeated n times: A000042 (k=1), A090843 (k=2), A097166 (k=3), A099914 (k=4), A099915 (k=5), this sequence (k=6), A246058 (k=7), A246059 (k=8), A067272 (k=9).

Cf. A002277, A093143.

Sequence in context: A204031 A025930 A125404 * A265598 A021744 A025445

Adjacent sequences:  A246054 A246055 A246056 * A246058 A246059 A246060

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Aug 13 2014

STATUS

approved

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Last modified March 18 17:51 EDT 2019. Contains 321292 sequences. (Running on oeis4.)