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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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..4.

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

Adjacent sequences:  A271499 A271500 A271501 * A271503 A271504 A271505

KEYWORD

nonn,base,more

AUTHOR

José de Jesús Camacho Medina, Apr 08 2016

STATUS

approved

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Last modified June 14 10:04 EDT 2021. Contains 345025 sequences. (Running on oeis4.)