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

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

References

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

Links

• 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).

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

Programs

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 *)

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)

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