

A080709


Take sum of squares of digits of previous term, starting with 4.


14



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
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OFFSET

1,1


COMMENTS

Terms of the simple continued fraction of 75798937186 / [sqrt(590163403297552587888099)749562250137].  Paolo P. Lava, Aug 06 2009
Occurs as puzzle in the Nintendo DS game "Professor Layton and the Diabolical Box".  M. F. Hasler, Dec 18 2009
From M. F. Hasler, Apr 27 2018: (Start)
As the orbit of 4 under A003132, this could rather have offset 0. Merges with the orbit of 5 at the 5th term of both sequences, and with other orbits as given in the formula section.
Porges gave his "set of eight numbers" as a(1)..a(8) in this order, rather than that of the set A039943. (End)


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), 379382.
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*(859*(n mod 8)+1027*((n+1) mod 8)+3295*((n+2) mod 8)1157*((n+3) mod 8)457*((n+4) mod 8)177*((n+5) mod 8)177*((n+6) mod 8)+75*((n+7) mod 8)).  Paolo P. Lava, Nov 27 2006
a(n) = A000216(n+1).  R. J. Mathar, Sep 19 2008
By definition, a(n+1) = A003132(a(n)) for n >= 1. a(n) = A000221(n) = A000218(n+3) = A008460(n+6) = A008462(n+1) = A008463(n+2) = A122065(n+3) = A139566(n+2) for n >= 8 or earlier.  M. F. Hasler, May 24 2009, edited Apr 27 2018


MATHEMATICA

NestList[Total[IntegerDigits[#]^2]&, 4, 80] (* Vincenzo Librandi, Jan 29 2013 *)


PROG

(PARI) A080709(n)=[4, 16, 37, 58, 89, 145, 42, 20][(n1)%8+1] \\ M. F. Hasler, May 24 2009
(Haskell)
a080709 n = a080709_list !! (n1)
a080709_list = iterate a003132 4
 Reinhard Zumkeller, Aug 24 2011
(MAGMA) &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, A000216 (starting with 2), A000218 (starting with 3), 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: A054246 A173545 A340233 * A256322 A080855 A203299
Adjacent sequences: A080706 A080707 A080708 * A080710 A080711 A080712


KEYWORD

nonn,base,easy


AUTHOR

N. J. A. Sloane, Mar 04 2003


STATUS

approved



