This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(2) = 4150 since 4^5 + 1^5 + 5^5 + 0^5 = 1024 + 1 + 3125 + 0 = 4150.
for(n=0,10^6,A055014(n)==n&&print1(n",")) \\ M. F. Hasler, Apr 12 2015
43 = 4^2 + 3^3; 254 = 2^7 + 5^3 + 4^0 = 128 + 125 + 1. 209 = 2^7 + 0^1 + 9^2. 732 = 7^0 + 3^6 + 2^1.
43 = 4^2 + 3^3; 254 = 2^7 + 5^3 + 4^0 = 128 + 125 + 1. 209 = 2^7 + 9^2. 732 = 7^0 + 3^6 + 2^1.
a061862 n = a061862_list !! (n-1)
a061862_list = filter f [0..] where
f x = g x 0 where
g 0 v = v == x
g u v = if d <= 1 then g u' (v + d) else v <= x && h 1
where h p = p <= x && (g u' (v + p) || h (p * d))
(u', d) = divMod u 10
-- Reinhard Zumkeller, Jun 02 2013
f[ n_ ] := Module[ {}, a=IntegerDigits[ n ]; e=g[ Length[ a ] ]; MemberQ[ Map[ Apply[ Plus, a^# ] &, e ], n ] ] g[ n_ ] := Map[ Take[ Table[ 0, {n} ]~Join~#, -n ] &, IntegerDigits[ Range[ 10^n ], 10 ] ] For[ n=0, n >= 0, n++, If[ f[ n ], Print[ n ] ] ]
For a(8)=7, the solutions are {1,16,17,256,257,272,273}. In base 8, these are written as {1, 20, 21, 400, 401, 420, 421}. Because 1^4 = 1, 2^4 + 0^4 = 16, 2^4 + 1^4 = 17, 4^4 + 0^4 + 0^4 = 256, etc., these are the fixed points in base 8.
inbase=function(n,b) { x=c(); while(n>=b) { x=c(n%%b,x); n=floor(n/b) }; c(n,x) }
yn=rep(NA,20)
for(b in 2:20) yn[b]=sum(sapply(1:(1.5*b^4),function(x) sum(inbase(x,b)^4))==1:(1.5*b^4)); yn
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