OFFSET
1,1
COMMENTS
Essentially the same as A080709, cf. formula. - M. F. Hasler, May 24 2009
As the orbit of 5 under A003132, this could as well start with index 0. - M. F. Hasler, Apr 27 2018
REFERENCES
R. Honsberger, Ingenuity in Mathematics, 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.
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 1).
FORMULA
Ultimately periodic with period 8.
a(n) = A080709(n) for n >= 5. - M. F. Hasler, May 24 2009
a(n+1) = A003132(a(n)). - Reinhard Zumkeller, Dec 19 2011
MATHEMATICA
NestList[Plus @@ IntegerDigits[ # ]^2 &, 5, 50]
PadRight[{5, 25, 29, 85}, 120, {4, 16, 37, 58, 89, 145, 42, 20}] (* Harvey P. Dale, Jan 14 2022 *)
PROG
(PARI) A000221(n)=[20, 4, 16, 37, 58, 89, 145, 42, 5, 25, 29, 85][n%8+8^(n<5)] \\ M. F. Hasler, May 24 2009, edited Apr 27 2018
(Magma) [5, 25, 29, 85] cat &cat[[89, 145, 42, 20, 4, 16, 37, 58]: n in [0..17]]; // Vincenzo Librandi, Jan 29 2013
(Haskell)
a000221 n = a000221_list !! (n-1)
a000221_list = iterate a003132 5
-- Reinhard Zumkeller, Mar 04 2013
CROSSREFS
Cf. A003132 (the iterated map), A003621, A039943, A099645, A031176, A007770, A000216 (starting with 2), A000218 (starting with 3), A080709 (starting with 4), 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,nice
AUTHOR
STATUS
approved