A000218 Take sum of squares of digits of previous term; start with 3.

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

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

Sequence in context: A018604 A301535 A215712 * A139731 A259986 A124049

Adjacent sequences: A000215 A000216 A000217 * A000219 A000220 A000221

Keyword

nonn,base,easy

Author

N. J. A. Sloane

Status

approved