A000221 Take sum of squares of digits of previous term; start with 5.

5, 25, 29, 85, 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, 58, 89, 145

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

Sequence in context: A070380 A068574 A000350 * A018612 A036127 A291755

Adjacent sequences: A000218 A000219 A000220 * A000222 A000223 A000224

Keyword

nonn,base,easy,nice

Author

N. J. A. Sloane

Status

approved