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A248970 Bases that lack a three-digit narcissistic number: numbers n with no 1 <= x < n, 0 <= y,z < n such that x^3 + y^3 + z^3 = n^2*x + n*y + z. 1
72, 90, 108, 153, 270, 423, 450, 531, 558, 630, 648, 738, 1044, 1098, 1125, 1224, 1242, 1287, 1440, 1503, 1566, 1611, 1620, 1800, 1935, 2034, 2142, 2250, 2358, 2439, 2448, 2511, 2754, 2790, 2799, 2862, 2943, 2952 (list; graph; refs; listen; history; text; internal format)
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

Cf. A005188 (base 10).

Sequence in context: A043187 A039364 A043967 * A066943 A206264 A063922

Adjacent sequences:  A248967 A248968 A248969 * A248971 A248972 A248973

KEYWORD

nonn,base

AUTHOR

Michael R Peake, Oct 18 2014

EXTENSIONS

a(26)-a(38) from Charles R Greathouse IV, Oct 21 2014

STATUS

approved

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Last modified April 26 08:46 EDT 2019. Contains 322472 sequences. (Running on oeis4.)