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A271502
Number with digits abc...z such that n = (a+b+c+...+z+a^b+b^c+c^d+...+y^z)+(a*b*c*...*z*a^b*b^c*c^d*...*y^z).
0
0, 18, 81, 1323
OFFSET
1,2
COMMENTS
Another variant of narcissistic numbers.
No other terms below 10^5.
a(5), if it exists, is > 3*10^10. - Lars Blomberg, Aug 08 2016
LINKS
José Camacho Medina's Matematico Fresnillense, Otra Variante de Números Narcisistas (in Spanish).
EXAMPLE
18 is a term because 18 = (1+8+1^8)+(1*8*1^8);
81 is a term because 81 = (8+1+8^1)+(8*1*8^1);
1323 is a term because 1323 = (1+3+2+3+1^3+3^2+2^3)+(1*3*2*3*1^3*3^2*2^3).
MATHEMATICA
CC = Table[( Sum[ Mod[(Floor[f/10^n]), 10] , {n, 0, Floor[Log[10, f]] }]), {f, 1, 1323}];
DD = Table[( Sum[ (Mod[(Floor[f/10^n]), 10] ) ^(Mod[(Floor[f/
10^(n - 1)]), 10] ) , {n, 1, Floor[Log[10, f]] }]), {f, 1, 1323}];
EE = Table[( Product[ Mod[(Floor[f/10^n]), 10] , {n, 0, Floor[Log[10, f]] }]), {f, 1, 555}];
FF = Table[( Product[ (Mod[(Floor[f/10^n]), 10] ) ^(Mod[(Floor[f/10^(n - 1)]), 10] ) , {n, 1, Floor[Log[10, f]] }]), {f, 1, 1323}];
SUMA = (CC+DD) + (EE*FF)
RES = SUMA - Table[n, {n, 1, 1323}]
Position[SS, 0]
CROSSREFS
Cf. A005188.
Sequence in context: A338039 A085504 A214531 * A235641 A087636 A156218
KEYWORD
nonn,base,more
AUTHOR
STATUS
approved