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A300081 a(n) is the number of steps needed to reach 1 or 89 under iteration of sum-of-squares-of-digits map. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

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

EXAMPLE

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.

PROG

(PARI) 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

CROSSREFS

Cf. A003621, A007770.

Sequence in context: A245655 A011497 A010488 * A293843 A240946 A343039

Adjacent sequences:  A300078 A300079 A300080 * A300082 A300083 A300084

KEYWORD

nonn,base

AUTHOR

Seiichi Manyama, Feb 24 2018

STATUS

approved

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Last modified May 5 17:26 EDT 2021. Contains 343572 sequences. (Running on oeis4.)