A193995 Maximum number of terms required to determine whether a number is happy or not (A007770 or A031177).

1, 9, 13, 8, 12, 17, 6, 13, 12, 2, 10, 13, 3, 14, 11, 8, 13, 11, 5, 8, 13, 14, 4, 9, 11, 10, 14, 4, 10, 13, 3, 4, 12, 12, 13, 16, 8, 10, 13, 9, 14, 8, 12, 5, 15, 12, 11, 14, 5, 12, 11, 11, 13, 15, 13, 10, 12, 8, 10, 17, 9, 10, 16, 12, 10, 15, 10, 3, 13, 6

Offset

1,2

Comments

The number 1 is the only term requiring just one term to determine if it is happy. Although the b-file appears to show that there are only a few numbers having 8 terms, see A193996 for more beginning at 78999.

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Example

For n=2, a(n)=9 because the iterations are 2, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16,...

Mathematica

f[n_] := Total[IntegerDigits[n]^2]; Table[Length[NestWhileList[f, n, UnsameQ, All]] - 1, {n, 100}]

Crossrefs

Sequence in context: A273614 A281224 A050236 * A070607 A340490 A335662

Adjacent sequences: A193992 A193993 A193994 * A193996 A193997 A193998

Keyword

nonn,base

Author

T. D. Noe, Aug 23 2011

Status

approved