A115026 Limiting value of n under iteration of "sum of the digits raised to the power of the number of digits of n" (A101337).

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 5, 1, 370, 370, 370, 370, 370, 1, 4, 5, 8, 1, 4, 370, 370, 370, 1, 370, 9, 1, 1, 370, 370, 370, 370, 370, 370, 370, 370, 370, 4, 370, 1, 370, 370, 370, 370, 1, 370, 370, 370, 370, 370, 370, 370, 370, 370, 160, 370, 370, 370, 370, 370, 370

Offset: 1

Author

Sergio Pimentel, Feb 24 2006

Keywords

• nonn
• base

Comments

Iterate A101337 starting at n until reaching a constant value (like 370) or a cycle (like 160, 217, 352, 160, ...). In the latter case, a(n) takes the smallest value in the cycle (e.g., a(59) = 160). Since k*9^k < 10^k for all k > 34, each number n is guaranteed to yield a smaller number a(n) if n > 10^34, so every number reaches a constant or a cycle under this sequence.

Conjecture: no term is greater than 370. - Harvey P. Dale, Jun 08 2022

Examples

			a(89)=370 since:
89 (2 digits): 8^2 + 9^2 = 145,
145 (3 digits): 1^3 + 4^3 + 5^3 = 190,
190 (3 digits): 1^3 + 9^3 + 0^3 = 730,
730 (3 digits): 7^3 + 3^3 + 0^3 = 370,
370 (3 digits): 3^3 + 7^3 + 0^3 = 370, etc.
So a(89) = 370 since 370 is a fixed point of A101337.
		

Crossrefs

Cf. A101337.

Programs

Mathematica

Table[Min[FindTransientRepeat[NestList[Total[IntegerDigits[#]^IntegerLength[#]]&,n,20],3][[2]]],{n,70}] (* Harvey P. Dale, Jun 08 2022 *)