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

1,1

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).

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]

Example

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).

Crossrefs

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

Sequence in context: A281241 A072884 A072889 * A165337 A256925 A235285

Adjacent sequences: A157711 A157712 A157713 * A157715 A157716 A157717

Keyword

base,nonn,fini

Author

Hans Havermann, Mar 04 2009

Status

approved