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A004186
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Arrange digits of n in decreasing order.
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41
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 21, 31, 41, 51, 61, 71, 81, 91, 20, 21, 22, 32, 42, 52, 62, 72, 82, 92, 30, 31, 32, 33, 43, 53, 63, 73, 83, 93, 40, 41, 42, 43, 44, 54, 64, 74, 84, 94, 50, 51, 52, 53, 54, 55, 65, 75, 85, 95, 60, 61, 62, 63, 64, 65, 66, 76, 86, 96, 70, 71, 72
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refs;
listen;
history;
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internal format)
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OFFSET
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0,3
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COMMENTS
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If we define "sortable primes" as prime numbers that remain prime when their digits are sorted in decreasing order, then all absolute primes (A003459) are sortable primes but not all sortable primes are absolute primes. For example, 113 is both sortable and absolute, and 313 is sortable but not absolute since its digits can be permuted to 133 = 7 * 19. - Alonso del Arte, Oct 05 2013
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LINKS
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EXAMPLE
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a(19) = 91 because the digits of 19 being 1 and 9, arranged in decreasing order they are 9 and 1.
a(20) = 20 because the digits are already in decreasing order.
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MAPLE
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local dgs;
convert(n, base, 10) ;
dgs := sort(%) ;
add( op(i, dgs)*10^(i-1), i=1..nops(dgs)) ;
end proc:
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MATHEMATICA
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sortDigitsDown[n_] := FromDigits@ Reverse@ Sort@ IntegerDigits@ n; Array[sortDigitsDown, 73, 0] (* Robert G. Wilson v, Aug 19 2011 *)
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PROG
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(PARI)
reconstruct(m) = {local(r); r=0; for(i=1, matsize(m)[2], r=r*10+m[i]); r}
A004186(n) = reconstruct(vecsort(digits(n), , 4))
(PARI) a(n) = fromdigits(vecsort(digits(n), , 4)); \\ Joerg Arndt, Feb 24 2019
(Haskell)
import Data.List (sort)
a004186 = read . reverse . sort . show :: Integer -> Integer
(Python)
def a(n): return int("".join(sorted(str(n), reverse=True)))
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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