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

1,2

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.

Mathematica

a[n_]:=Module[{k=0, x=n}, While[x!=1&&x!=89, k++; x=Total[IntegerDigits[x]^2]]; k]; Array[a, 89] (* James C. McMahon, Feb 28 2026 *)

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