A003621 -id:A003621 - cp's OEIS frontend

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

N. J. A. Sloane

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

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).

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

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 *)

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)

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

A300081 a(n) is the number of steps needed to reach 1 or 89 under iteration of sum-of-squares-of-digits map.

Original entry on oeis.org

0, 5, 7, 4, 4, 9, 5, 5, 6, 1, 6, 5, 2, 6, 6, 3, 5, 5, 4, 5, 5, 6, 3, 6, 3, 5, 6, 3, 2, 7, 2, 3, 6, 4, 5, 8, 2, 3, 7, 4, 6, 6, 4, 4, 7, 4, 5, 6, 4, 4, 6, 3, 5, 7, 5, 4, 6, 1, 4, 9, 3, 5, 8, 4, 4, 7, 2, 2, 8, 5, 5, 6, 2, 5, 6, 2, 9, 8, 3, 5, 5, 3, 3, 6, 1, 2, 8, 10, 0

Offset: 1

Seiichi Manyama, Feb 24 2018

By the definition, a(1) = a(89) = 0.

			n|  0     1     2     3     4     5     6     7     8     9
-----------------------------------------------------------
2|  2 ->  4 -> 16 -> 37 -> 58 -> 89.
3|  3 ->  9 -> 81 -> 65 -> 61 -> 37 -> 58 -> 89.
4|  4 -> 16 -> 37 -> 58 -> 89.
5|  5 -> 25 -> 29 -> 85 -> 89.
6|  6 -> 36 -> 45 -> 41 -> 17 -> 50 -> 25 -> 29 -> 85 -> 89.

Seiichi Manyama, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Happy Number
Eric Weisstein's World of Mathematics, Unhappy Number
Wikipedia, Happy number

Cf. A003621, A007770.

f(n) = {my(d = digits(n)); sum(k=1, #d, d[k]^2);}
a(n) = {my(nb = 0, fn = n); while (! ((n == 1) || (n == 89)), n = f(n); nb++); nb;} \\ Michel Marcus, Feb 25 2018

cp's OEIS Frontend

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

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