A008463 Take sum of squares of digits of previous term; start with 9.

9, 81, 65, 61, 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, 58, 89, 145

Offset

1,1

References

R. Honsberger, Ingenuity in Mathematics, Random House, 1970, p. 83.

Links

Table of n, a(n) for n=1..72.

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) = A000218(n+1). - R. J. Mathar, May 24 2008

a(n) = A080709(n-2) for n > 4. - M. F. Hasler, May 24 2009

Mathematica

Nest[Append[#, Total[IntegerDigits[Last@ #]^2]] &, {9}, 79] (* Michael De Vlieger, Apr 29 2018 *)
NestList[Total[IntegerDigits[#]^2]&, 9, 80] (* or *) PadRight[ {9, 81, 65, 61}, 80, {42, 20, 4, 16, 37, 58, 89, 145}] (* Harvey P. Dale, Sep 11 2019 *)

Prog

From M. F. Hasler, May 24 2009: (Start)
(PARI) A008463(n)=[9, 81, 65, 61, 37, 58, 89, 145, 42, 20, 4, 16][if(n>12, (n-5)%8+5, n)]
/* This code has been checked as follows: */
k=3; vector(99, n, k=A003132(k))==vector(99, n, A008463(n))
/* The given terms have been checked as follows: */
a=[/* paste the terms here */]; apply(A008463, [1..#a])==a \\ (End)

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), 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: A107346 A209280 A014393 * A203656 A043087 A037414

Adjacent sequences: A008460 A008461 A008462 * A008464 A008465 A008466

Keyword

nonn,base,easy

Author

N. J. A. Sloane

Status

approved