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A000216 Take sum of squares of digits of previous term. 19
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.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..100

H. G. Grundmann, Semihappy Numbers, J. Int. Seq. 13 (2010), 10.4.8, Theorem 1.

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

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. - 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)] \\ 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). - M. F. Hasler, May 24 2009

Sequence in context: A247219 A265835 A185074 * A110998 A051861 A290265

Adjacent sequences:  A000213 A000214 A000215 * A000217 A000218 A000219

KEYWORD

nonn,base,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 22 07:02 EDT 2017. Contains 290943 sequences.