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A000218
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Take sum of squares of digits of previous term.
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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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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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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)=[3, 9, 81, 65, 61, 37, 58, 89, 145, 42, 20, 4, 16][n%8+(n%8<6 & n>7)*8] \\ M. F. Hasler, May 24 2009
(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: A032330 A018604 A215712 * A139731 A259986 A124049
Adjacent sequences: A000215 A000216 A000217 * A000219 A000220 A000221
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KEYWORD
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nonn,base,easy,changed
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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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