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A240511 Numbers that are equal to the sum of their digits raised to each power from 1 to the number of digits. 1
1, 2, 3, 4, 5, 6, 7, 8, 9, 90, 336, 4538775, 183670618662, 429548754570, 3508325641459, 3632460407839, 9964270889420, 10256010588126, 509608423720931, 589543349257828, 75363159369591953, 108765782844884700, 360449417601592380, 1574414276673927523 (list; graph; refs; listen; history; text; internal format)
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: A278944 A024664 A078188 * A198486 A061805 A280658

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

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Last modified August 21 17:48 EDT 2017. Contains 290892 sequences.