editing

approved

H. Havermann, <a href="/A157714/a157714.png">Self-serving altruistic numbers</a> [Cached copy, with permission]

approved

editing

editing

approved

E. Angelini, <a href="/A151543/a151543.pdf">A Recurring Digital Invariant Variant</a> [Cached, with permission]

approved

editing

_Hans Havermann (gladhobo(AT)teksavvy.com), _, Mar 04 2009

Hans Havermann (pxpgladhobo(AT)rogersteksavvy.com), Mar 04 2009

Hans Havermann, <a href="/A157714/b157714.txt">Table of n, a(n) for n=1..265</a>

base,nonn,fini,new

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

1,1

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).

Hans Havermann, <a href="b157714.txt">Table of n, a(n) for n=1..265</a>

E. Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/RecurDigit.htm">A Recurring Digital Invariant variant</a>

H. Havermann, <a href="http://chesswanks.com/blahg/odo/Blog/Entries/2009/2/27_Self-serving_altruistic_numbers.html">Self-serving altruistic numbers</a>

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).

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

base,nonn,fini

Hans Havermann (pxp(AT)rogers.com), Mar 04 2009

approved