A008462 Take sum of squares of digits of previous term; start with 8.

8, 64, 52, 29, 85, 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, 58, 89, 145

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

Arthur Porges, A set of eight numbers, Amer. Math. Monthly 52 (1945), 379-382.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 1).

Formula

Periodic with period 8.

a(n) = A080709(n-1) for n >= 5 and a(n) = A000221(n-1) = A008460(n+4) for all n >= 4. - M. F. Hasler, May 24 2009; edited and extended Apr 27 2018

From Colin Barker, Apr 28 2018: (Start)

G.f.: x*(8 + 64*x + 52*x^2 + 29*x^3 + 85*x^4 + 89*x^5 + 145*x^6 + 42*x^7 + 12*x^8 - 60*x^9 - 36*x^10 + 8*x^11 - 27*x^12) / ((1 - x)*(1 + x)*(1 + x^2)*(1 + x^4)).

a(n) = a(n-8) for n>13.

(End)

Mathematica

NestList[Total[IntegerDigits[#]^2]&, 8, 80] (* Vincenzo Librandi, Jan 29 2013 *)
PadRight[{8, 64, 52, 29, 85}, 80, {20, 4, 16, 37, 58, 89, 145, 42}] (* Harvey P. Dale, Dec 27 2019 *)

Prog

(PARI) A008462(n)=[8, 64, 52, 29, 85, 89, 145, 42, 20, 4, 16, 37, 58][if(n>13, (n-6)%8+6, n)] \\ M. F. Hasler, May 24 2009
(Magma) [8, 64, 52, 29, 85] cat &cat[[89, 145, 42, 20, 4, 16, 37, 58]: n in [0..17]]; // Vincenzo Librandi, Jan 29 2013
(PARI) Vec(x*(8 + 64*x + 52*x^2 + 29*x^3 + 85*x^4 + 89*x^5 + 145*x^6 + 42*x^7 + 12*x^8 - 60*x^9 - 36*x^10 + 8*x^11 - 27*x^12) / ((1 - x)*(1 + x)*(1 + x^2)*(1 + x^4)) + O(x^60)) \\ Colin Barker, Apr 28 2018

Crossrefs

Cf. A003132 (the iterated map), A003621, A039943, A099645, A031176, A007770, A000216 (starting with 2), A000218 (starting with 3), A080709 (starting with 4), A000221 (starting with 5), A008460 (starting with 6), A008463 (starting with 9), A139566 (starting with 15), A122065 (starting with 74169). - M. F. Hasler, May 24 2009

Sequence in context: A137664 A317028 A014392 * A043078 A037413 A107626

Adjacent sequences: A008459 A008460 A008461 * A008463 A008464 A008465

Keyword

nonn,base,easy

Author

N. J. A. Sloane

Status

approved