A000216 Take sum of squares of digits of previous term, starting with 2.

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

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

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.

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.

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)=[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

Adjacent sequences: A000213 A000214 A000215 * A000217 A000218 A000219

Keyword

nonn,base,easy

Author

N. J. A. Sloane

Status

approved