A226064 Largest fixed point in base n for the sum of the fourth power of its digits.
1, 1, 243, 419, 1, 1, 273, 1824, 9474, 10657, 1, 8194, 1, 53314, 47314, 36354, 1, 246049, 53808, 378690, 170768, 185027, 1, 247507, 1, 1002324, 722739, 278179, 301299, 334194, 1004643, 959859, 1, 1538803, 1798450, 1, 4168450, 2841074, 1, 1877793, 5556355
Offset: 2
Examples
The fixed points in base 8 are {1,16,17,256,257,272,273}, because in base 8, these are written as {1,20,21,400,401,420,421} and 1^4 = 1, 2^4 + 0^4 = 16, 2^4 + 1^4 = 17, 4^4 + 0^4 + 0^4 = 256, etc. The largest of these is 273 = a(8).
Links
- Christian N. K. Anderson, Table of n, a(n) for n = 2..250
- Christian N. K. Anderson, Table of base, largest fixed point, number of fixed points, and a list of all fixed points in base 10 and base n for n = 1..250
Crossrefs
Programs
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R
for(b in 2:50) { fp=c() for(w in 1:b-1) for(x in 1:b-1) if((v1=w^4+x^4)<=(v2=w*b^3+x*b^2)) for(y in 1:b-1) if((u1=v1+y^4)<=(u2=v2+y*b) & u1+b^4>u2+b-1) { z=which(u1+(1:b-1)^4==u2+(1:b-1))-1 if(length(z)) fp=c(fp,u2+z) } cat("Base",b,":",fp[-1],"\n") }
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