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

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

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).

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

Programs

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

Mathematica

NestList[Total[IntegerDigits[#]^2]&, 3, 80] (* Vincenzo Librandi, Jan 29 2013 *)

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

Formula

Eventually periodic with period 8.