A270540 Numbers that are equal to the number of their digits multiplied by the sum of the fifth powers of the digits.

0, 1, 1232, 4100, 268542

Offset

1,3

Comments

Terms up to 10^8.

No further terms after 10^7 since 10^k > k^2*9^5 beyond that point. - Ray Chandler, Apr 01 2016

Links

Table of n, a(n) for n=1..5.

Example

4100 is a term because 4100 = 4*(4^5+1^5+0^5+0^5).

Mathematica

Position[ Table[ IntegerLength[ k] Sum[( Floor[k/10^n] - 10 Floor[k/10^(n + 1)])^5, {n, 0, IntegerLength@ k}] - k, {k, 1, 10^6}], 0] // Flatten = {1, 1232, 4100, 268542}
Select[Range[10^7], With[{id=IntegerDigits[#]}, #==Length[id]*Plus@@(id^5)]&] (* Ray Chandler, Apr 01 2016 *)

Prog

(PARI) isok(n) = my(d=digits(n)); n == #d*sum(k=1, #d, d[k]^5); \\ Michel Marcus, Mar 25 2016

Crossrefs

Cf. A055014.

Sequence in context: A278018 A182721 A183881 * A206272 A064942 A101311

Adjacent sequences: A270537 A270538 A270539 * A270541 A270542 A270543

Keyword

nonn,base,fini,full

Author

José de Jesús Camacho Medina, Mar 18 2016

Extensions

a(5) from Michel Marcus, Mar 25 2016

Status

approved