A240511 Numbers that are equal to the sum of their digits raised to each power from 1 to the number of digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 90, 336, 4538775, 183670618662, 429548754570, 3508325641459, 3632460407839, 9964270889420, 10256010588126, 509608423720931, 589543349257828, 75363159369591953, 108765782844884700, 360449417601592380, 1574414276673927523

Offset

1,2

Comments

Numbers with only 0 and 1 as digits are not considered. - Paolo P. Lava, Jan 11 2017

Links

Giovanni Resta, Table of n, a(n) for n = 1..54 (terms < 10^32)

José de Jesús Camacho Medina, Misterio de Números

Formula

f(n) = Sum_{i,1,floor(log_10(n))+1} (Sum_{k,0,floor(log_10(n))+1} (floor(n/10^k) - 10*floor(n/10^(k + 1)))^(i)). If f(n)-n=0 then n is a number of this category. - José de Jesús Camacho Medina, Apr 07 2014

Example

9 = (9^1).
90 = (9^1 + 0^1) + (9^2 + 0^2).
336 = (3^1 + 3^1 + 6^1) + (3^2 + 3^2 + 6^2) + (3^3 + 3^3 + 6^3).

Mathematica

Q = Table[Sum[(Sum[(Floor[f/10^n] - 10*Floor[f/10^(n + 1)])^(i), {n, 0, Floor[Log[10, f]] + 1}]), {i, 1, Floor[Log[10, f]] + 1}], {f, 336}] - Range[336]; Flatten@ Position[Q, 0]
Select[Range[10^3], Plus @@ Power @@@ Tuples[{IntegerDigits @ #, Range@ IntegerLength@ #}] == # &] (* Giovanni Resta, Apr 30 2014 *)

Prog

(PARI) isok(n) = (d = digits(n)) && (n == sum(i=1, #d, sum(j=1, #d, d[j]^i))); \\ Michel Marcus, Apr 07 2014

Crossrefs

Sequence in context: A338831 A024664 A078188 * A345406 A198486 A061805

Adjacent sequences: A240508 A240509 A240510 * A240512 A240513 A240514

Keyword

nonn,base,fini

Author

José de Jesús Camacho Medina, Apr 06 2014

Extensions

a(12)-a(24) from Giovanni Resta, Apr 07 2014

Status

approved