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A000218
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Take sum of squares of digits of previous term; start with 3.
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16
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3, 9, 81, 65, 61, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Could also have offset 0, considered as the orbit of 3 under A003132, i.e., n-fold application of A003132 on the initial value 3. - M. F. Hasler, Apr 27 2018
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REFERENCES
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R. Honsberger, Ingenuity in Math., Random House, 1970, p. 83.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..100
Arthur Porges, A set of eight numbers, Amer. Math. Monthly 52 (1945), 379-382.
A. Porges, A set of eight numbers, Amer. Math. Monthly, 52 (1945), 379-382. [Annotated scanned copy]
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 1).
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FORMULA
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Eventually periodic with period 8.
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MATHEMATICA
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NestList[Total[IntegerDigits[#]^2]&, 3, 80] (* Vincenzo Librandi, Jan 29 2013 *)
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PROG
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(PARI) A000218(n)=[89, 145, 42, 20, 4, 16, 37, 58, 3, 9, 81, 65, 61][n%8+8^(n<6)] \\ M. F. Hasler, May 24 2009, edited Apr 27 2018
(Haskell)
a000218 n = a000218_list !! (n-1)
a000218_list = iterate a003132 3
-- Reinhard Zumkeller, Aug 24 2011
(MAGMA) [3, 9, 81, 65, 61] cat &cat[[37, 58, 89, 145, 42, 20, 4, 16]: n in [0..17]]; // Vincenzo Librandi, Jan 29 2013
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CROSSREFS
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Cf. A003132 (the iterated map), A003621, A039943, A099645, A031176, A007770, A000216 (starting with 2), A080709 (starting with 4), A000221 (starting with 5), A008460 (starting with 6), A008462 (starting with 8), A008463 (starting with 9), A139566 (starting with 15), A122065 (starting with 74169). - M. F. Hasler, May 24 2009
Sequence in context: A018604 A301535 A215712 * A139731 A259986 A124049
Adjacent sequences: A000215 A000216 A000217 * A000219 A000220 A000221
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KEYWORD
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nonn,base,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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