A157714 Base-10 pseudo-altruistic numbers.

136, 160, 217, 244, 259, 352, 496, 586, 664, 736, 853, 862, 1009, 2178, 2929, 3233, 3283, 4274, 4394, 6514, 6562, 7154, 10933, 13154, 18829, 50062, 58618, 59536, 73318, 76438, 124618, 282595, 312962, 329340, 376761, 537059, 578955, 681069

Offset: 1

Author

Hans Havermann, Mar 04 2009

Keywords

• base
• nonn
• fini

Comments

These integers reoccur (with a period greater than 1) upon the iteration of raising every digit to the power of the number's length and summing.

If the reoccurrence is immediate (period 1), the numbers are (instead) narcissistic (A005188).

Examples

			2929 is pseudo-altruistic because 2929 -> 13154 (2^4 + 9^4 + 2^4 + 9^4) -> 4394 (1^5 + 3^5 + 1^5 + 5^5 + 4^5) -> 7154 (4^4 + 3^4 + 9^4 + 4^4) -> 3283 (7^4 + 1^4 + 5^4 + 4^4) -> 4274 (3^4 + 2^4 + 8^4 + 3^4) -> 2929 (4^4 + 2^4 + 7^4 + 4^4).
		

Links

• Hans Havermann, Table of n, a(n) for n=1..265
• E. Angelini, A Recurring Digital Invariant variant
• E. Angelini, A Recurring Digital Invariant Variant [Cached, with permission]
• H. Havermann, Self-serving altruistic numbers
• H. Havermann, Self-serving altruistic numbers [Cached copy, with permission]

Crossrefs

Cf. A005188. The "Recurring Digital Invariant Variant" is described in more detail in A151543.