OFFSET
1,1
COMMENTS
All terms are multiples of 9.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..296
StackExchange, Proof that all terms are multiples of 9
Eric Weisstein's World of Mathematics, Narcissistic Number
Wikipedia, Narcissistic number
EXAMPLE
17=1^3+2^3+2^3 is 122 in base 3, so 3 is not in the sequence.
PROG
(MATLAB) for Base=1:100, Noneyet=1; for a=1:Base-1, for b=0:Base-1, for c=0:Base-1, if a*Base*Base+b*Base+c==a^3+b^3+c^3, Noneyet = 0; end; end; end; end; if Noneyet, disp(Base); end; end;
(PARI) is(n)=if(n%9, return(0)); for(x=1, n-1, for(y=0, x, for(z=0, y, my(v=digits(x^3+y^3+z^3, n)); if(vecsort(v)==[z, y, x], return(0))))); 1 \\ slow; Charles R Greathouse IV, Oct 21 2014
(PARI) is(n)=if(n%9, return(0)); my(mx=n*(n-1)*(n-2), t); for(x=1, n-1, for(y=0, n-1, t=n*(n*x+y)-x^3-y^3; if(t>=0 && t <= mx && !polisirreducible('z^3-'z-t) && #select(P->poldegree(P)==1&&polcoeff(P, 0)<=0 && polcoeff(P, 0)>-n, factor('z^3-'z-t)[, 1]), return(0)))); 1 \\ faster; Charles R Greathouse IV, Oct 21 2014
CROSSREFS
KEYWORD
nonn,base,changed
AUTHOR
Michael R Peake, Oct 18 2014
EXTENSIONS
a(26)-a(38) from Charles R Greathouse IV, Oct 21 2014
STATUS
approved