login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A000216 Take sum of squares of digits of previous term, starting with 2. 20
2, 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, 42, 20, 4, 16, 37 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
As the orbit of 2 under A003132, this could also have offset 0. Merges into A080709 right after the first term: a(n+1) = A080709(n) for all n >= 1. - M. F. Hasler, Apr 27 2018
REFERENCES
R. Honsberger, Ingenuity in Mathematics, Random House, 1970, p. 83.
P. Kiss, A generalization of a problem in number theory, Math. Sem. Notes Kobe Univ., 5 (1977), no. 3, 313-317. MR 0472667 (57 #12362).
LINKS
H. G. Grundmann, Semihappy Numbers, J. Int. Seq. 13 (2010), 10.4.8, Theorem 1.
P. Kiss, A generalization of a problem in number theory, [Hungarian], Mat. Lapok, 25 (No. 1-2, 1974), 145-149.
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]
H. J. J. te Riele, Iteration of number-theoretic functions, Nieuw Archief v. Wiskunde, (4) 1 (1983), 345-360.
FORMULA
Periodic with period 8.
MATHEMATICA
NestList[Total[IntegerDigits[#]^2]&, 2, 80] (* Vincenzo Librandi, Jan 29 2013 *)
PROG
(PARI) A000216(n)=[42, 20, 4, 16, 37, 58, 89, 145, 2][n%8+8^(n<2)] \\ M. F. Hasler, May 24 2009, edited Apr 27 2018
(Haskell) a000216 n = a000216_list !! (n-1)
a000216_list = iterate a003132 2 -- Reinhard Zumkeller, Aug 24 2011
(Magma) [2] cat &cat[[4, 16, 37, 58, 89, 145, 42, 20]: n in [0..17]]; // Vincenzo Librandi, Jan 29 2013
CROSSREFS
Cf. A003132 (the iterated map), A003621, A039943, A099645, A031176, A007770, A000218 (starting with 3), 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: A247219 A265835 A185074 * A110998 A051861 A296297
KEYWORD
nonn,base,easy
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)