OFFSET
1,1
COMMENTS
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
REFERENCES
R. Honsberger, Ingenuity in Math., Random House, 1970, p. 83.
LINKS
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).
FORMULA
Eventually periodic with period 8.
MATHEMATICA
NestList[Total[IntegerDigits[#]^2]&, 3, 80] (* Vincenzo Librandi, Jan 29 2013 *)
PROG
(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
CROSSREFS
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
KEYWORD
nonn,base,easy
AUTHOR
STATUS
approved