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A246057 a(n) = (5*10^n - 2)/3. 11
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
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.
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).
Sequence in context: A341084 A025930 A125404 * A265598 A021744 A025445
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Aug 13 2014
STATUS
approved

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Last modified April 24 00:30 EDT 2024. Contains 371917 sequences. (Running on oeis4.)