A360697 The sum of the squares of the digits of n, repeated until reaching a single-digit number.

0, 1, 4, 9, 4, 4, 4, 1, 4, 4, 1, 2, 5, 1, 4, 4, 4, 4, 4, 1, 4, 5, 8, 1, 4, 4, 4, 4, 1, 4, 9, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 4, 4, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 4, 1, 4, 4, 4, 4, 4, 4, 4, 2, 1, 4, 4, 1, 4, 4, 4, 1, 2, 4, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1

Offset: 0

Author

Will Nicholes, Feb 16 2023

Keywords

• nonn
• base

Comments

Square the digits of n, then sum the squares. Repeat the process until the sum is less than 10.

Examples

			For n=28, the sum of the squares of the digits gives 4+64 = 68. Repeating the process gives 36+64 = 100; repeating once more gives 1+0+0 = 1. Therefore a(28) is 1.
a(n) = 4 for 72 of the first 100 n (0 to 99 inclusive.)
		

Crossrefs

Cf. A003132, A007770, A099645.

Programs

Mathematica

f[n_] := Plus @@ (IntegerDigits[n]^2); a[n_] := NestWhile[f, f[n], # > 9 &]; Array[a, 100, 0] (* Amiram Eldar, Feb 17 2023 *)