A383646 Smallest number that takes n steps to reach 1 under iteration of sum-of-cubes-of-digits map.

1, 10, 112, 1189, 778, 13477, 2388889999999999999999

Offset: 0

Author

Shyam Sunder Gupta, May 11 2025

Keywords

• nonn
• base

Comments

These could also be called the smallest cubic happy numbers of height n.

Subsequent terms are too large to display in full.

a(7) = 1127 * 10^3276941015089163237 - 1 (1126 followed by 3276941015089163237 nines).

a(8) = 35678 * 10^((a(7) - 1054)/729) - 1.

Examples

			a(2) = 112, because 112 takes 2 steps to reach 1 (112 --> 1 + 1 + 8 = 10 --> 1 + 0 = 1).
		

Links

• H. G. Grundman and E. A. Teeple, Heights of happy numbers and cubic happy numbers, Fib Quart. 41 (4) (2003) 301-306.
• Shyam Sunder Gupta, Happy Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 7, 209-222.

Crossrefs

Cf. A007770, A001273, A035504.