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

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

Author

Seiichi Manyama, Feb 24 2018

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

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

Crossrefs

Cf. A003621, A007770.

Programs

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