|
| |
|
|
A000216
|
|
Take sum of squares of digits of previous term.
|
|
18
|
|
|
|
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
|
|
|
REFERENCES
|
R. Honsberger, Ingenuity in Math., Random House, 1970, p. 83.
A. Porges, A set of eight numbers, Amer. Math. Monthly, 52 (1945), 379-382.
|
|
|
LINKS
|
Vincenzo Librandi, Table of n, a(n) for n = 1..100
|
|
|
FORMULA
|
Periodic with period 8.
a(n)=(1/224)*{1027*(n mod 8)+3295*[(n+1) mod 8]-1157*[(n+2) mod 8]-457*[(n+3) mod 8]-177*[(n+4) mod 8]-177*[(n+5) mod 8]+75*[(n+6) mod 8]+859*[(n+7) mod 8]}-18*[C(2*n,n) mod 2], with n>=0 [From Paolo P. Lava, Oct 21 2008]
|
|
|
MATHEMATICA
|
NestList[Total[IntegerDigits[#]^2]&, 2, 80] (* Vincenzo Librandi, Jan 29 2013 *)
|
|
|
PROG
|
(PARI) A000216(n)=[2, 4, 16, 37, 58, 89, 145, 42, 20][n%8+8*(n%8<2 & n>1)] \\\\ [From M. F. Hasler, May 24 2009]
(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). [From M. F. Hasler, May 24 2009]
Sequence in context: A074411 A189838 A185074 * A110998 A051861 A223093
Adjacent sequences: A000213 A000214 A000215 * A000217 A000218 A000219
|
|
|
KEYWORD
|
nonn,base,easy
|
|
|
AUTHOR
|
N. J. A. Sloane.
|
|
|
STATUS
|
approved
|
| |
|
|
