A211654 -id:A211654 - cp's OEIS frontend

A004185 Arrange digits of n in increasing order, then (for n > 0) omit the zeros.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 11, 12, 13, 14, 15, 16, 17, 18, 19, 2, 12, 22, 23, 24, 25, 26, 27, 28, 29, 3, 13, 23, 33, 34, 35, 36, 37, 38, 39, 4, 14, 24, 34, 44, 45, 46, 47, 48, 49, 5, 15, 25, 35, 45, 55, 56, 57, 58, 59, 6, 16, 26, 36, 46, 56, 66, 67, 68, 69, 7, 17, 27, 37, 47

Offset: 0

N. J. A. Sloane

Record values: A009994. - Reinhard Zumkeller, Dec 05 2009
If we define "sortable primes" as prime numbers that remain prime when their digits are sorted in increasing order, then all absolute primes (A003459) are sortable primes but not all sortable primes are absolute primes. For example, 311 is both sortable and absolute, and 271 is sortable but not absolute, since its digits can be permuted to 217 = 7 * 31 or 712 = 2^3 * 89, etc. - Alonso del Arte, Oct 05 2013
The above mentioned "sortable primes" are listed in A211654, the nontrivial ones (with digits not in nondecreasing order) in A086042. - M. F. Hasler, Jul 30 2019

			a(19) = 19 because the digits are already in increasing order.
a(20) = 2 because the digits of 20 are 2 and 0, which in increasing order are 0 and 2, but since zero-padding is not allowed on the left, the zero digit is dropped and we are left with 2.
a(21) = 12 because the digits of 21 are 2 and 1, which in increasing order are 1 and 2.

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A004719, A004151, A004086, A004186, A009996, A221714, A073138, A193581, A193582, A065641.

Cf. A211654 (sortable primes) and subsequence A086042 (nontrivial solutions).

import Data.List (sort)
a004185 n = read $ sort $ show n :: Integer
-- Reinhard Zumkeller, Aug 10 2011

A004185:=func; [n eq 0 select 0 else A004185(n): n in [0..57]]; // Bruno Berselli, Apr 03 2012

A004185 := proc(n)
    local dgs;
    convert(n,base,10) ;
    dgs := sort(%,`>`) ;
    add( op(i,dgs)*10^(i-1),i=1..nops(dgs)) ;
end proc:
seq(A004185(n),n=0..20) ; # R. J. Mathar, Jul 26 2015

FromDigits[Sort[DeleteCases[IntegerDigits[#], 0]]]&/@Range[0, 60] (* Harvey P. Dale, Nov 29 2011 *)

a(n)=fromdigits(vecsort(digits(n))) \\ Charles R Greathouse IV, Feb 06 2017

def A004185(n):
    return int(''.join(sorted(str(n))).replace('0','')) if n > 0 else 0 # Chai Wah Wu, Nov 10 2015

A086042 Nontrivial numbers which are prime and yield another prime when their digits are sorted in ascending order.

Original entry on oeis.org

31, 71, 73, 97, 101, 103, 107, 109, 131, 173, 193, 197, 271, 293, 307, 311, 317, 373, 397, 419, 439, 491, 509, 547, 571, 593, 607, 617, 647, 659, 673, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 809, 839, 907, 919, 937, 941, 947, 953, 971, 983, 991

Offset: 1

Chuck Seggelin, Jul 07 2003

Primes with digits already in ascending order (like 13 and 2357) are trivial cases and are therefore excluded.

See A211654 for the sequence including the trivial cases. - M. F. Hasler, Jul 30 2019

			a(1)=31 because an ascending sort of 31's digits yields 13 which is also prime. a(53)=1009 because an ascending sort of 1009's digits yields 19 which is also prime.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A086402, A086051, A211654.

[p:p in PrimesUpTo(1000)|  IsPrime(Seqint(Reverse(Sort(Intseq(p,10))))) and p ne Seqint(Reverse(Sort(Intseq(p,10)))) ]; // Marius A. Burtea, Jul 30 2019

paoQ[n_]:=Module[{idn=IntegerDigits[n],sidn},sidn=Sort[idn];sidn!=idn && PrimeQ[FromDigits[sidn]]] (* Harvey P. Dale, Nov 14 2011 *)

select( is_A086042(p,q=fromdigits(vecsort(digits(p))))={p>q&&isprime(q)&&isprime(p)}, [1..999]) \\ M. F. Hasler, Jul 30 2019

A182150 Semiprimes that are also semiprime when their digits are sorted into nondecreasing order.

Original entry on oeis.org

4, 6, 9, 14, 15, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 62, 69, 77, 85, 93, 94, 111, 115, 118, 119, 122, 123, 129, 133, 134, 143, 145, 146, 155, 158, 159, 166, 169, 177, 178, 185, 187, 202, 205, 206, 213, 219, 221, 226, 235, 237, 247, 249, 253

Offset: 1

Jonathan Vos Post, Apr 18 2012

This is to A211654 primes that are also prime when their digits are sorted into nondecreasing order as A001358 semiprimes are to A000040 primes. There is an ambiguity arising from OEIS conventions, exemplified by the semiprime 303, which sorts to 033 and truncates to the semiprime 33.

			51 is in the sequence because, though it is a semiprime whose digits are in descending order, once the digits are sorted to be nondecreasing, it is the semiprime 15, whose digits are (left to right) nondecreasing.

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Cf. A001358, A097393, A211654.

h:= proc(m) local k; for k from m+1 while isprime(k) or
            add(i[2], i=ifactors(k)[2])<>2 do od; k
    end:
a:= proc(n) option remember; local k, l, s;
      k:= h(a(n-1));
      do l:= sort(convert(k, base, 10));
         s:= add(l[i]*10^(nops(l)-i), i=1..nops(l));
         if h(s-1)=s then return k else k:=h(k) fi
      od
    end: a(0):=0:
seq(a(n), n=1..100);  # Alois P. Heinz, Apr 22 2012

Select[Range[300],PrimeOmega[#]==2&&PrimeOmega[FromDigits[ Sort[ IntegerDigits[ #]]]]==2&] (* Harvey P. Dale, Nov 13 2014 *)

More terms from Alois P. Heinz, Apr 22 2012

A211655 Down-sortable primes: Primes that are also primes after digits are sorted into decreasing order.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 31, 37, 41, 43, 53, 61, 71, 73, 79, 83, 97, 113, 131, 149, 157, 163, 167, 179, 181, 191, 197, 199, 211, 241, 251, 281, 311, 313, 331, 337, 347, 359, 373, 389, 419, 421, 431, 433, 443, 461, 463, 491, 521, 541, 563, 571, 593, 613, 617, 631, 641, 643, 653

Offset: 1

Francis J. McDonnell, Apr 17 2012

All 1- and 2-digit reversible primes (A007500) are trivially in this sequence. No primes from A056709 are in this sequence. Clearly all absolute primes (A003459) are sortable primes but not all sortable primes are absolute primes. - Alonso del Arte, Oct 08 2013

			131 is prime and after sorting its digits into nonincreasing order we obtain 311, which is prime.
163 is in the sequence because its digits sorted in decreasing order give 631, which is prime. (Note that this is not a reversible prime, since 361 = 19^2.)

Francis J. McDonnell, Table of n, a(n) for n = 1..10000
Francis J. McDonnell, Java Program

Cf. A004186, A211654, A028864, A028867.

Select[Prime[Range[200]], PrimeQ[FromDigits[-Sort[-IntegerDigits[#]]]] &] (* T. D. Noe, Apr 17 2012 *)

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A004185 Arrange digits of n in increasing order, then (for n > 0) omit the zeros.

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A086042 Nontrivial numbers which are prime and yield another prime when their digits are sorted in ascending order.

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A182150 Semiprimes that are also semiprime when their digits are sorted into nondecreasing order.

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A211655 Down-sortable primes: Primes that are also primes after digits are sorted into decreasing order.

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