A028906 -id:A028906 - cp's OEIS frontend

A326953 a(n) = A001222(A028906(n)).

1, 1, 1, 1, 1, 1, 1, 2, 5, 3, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 1, 1, 1, 3, 1, 3, 3, 3, 4, 1, 2, 1, 2, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 3, 3, 2, 3, 3, 1, 1, 5, 4, 3, 2, 3, 1, 7, 3, 3, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 1, 1, 1, 2, 1, 5, 3, 1, 1, 3, 2, 3, 1, 3, 3, 4, 1, 4, 1

Offset: 1

Joshua Michael McAteer, Aug 06 2019

Multiplicity of prime divisors of n, where n is a number composed of the reverse sorted digits of a prime number.

Conjecture: the sum of the first n terms of A326953 (largest to smallest sorting) is >= the sum of the first n terms of A326952 (smallest to largest sorting). This is true for the first 9592 terms.

			The 28th prime number is 107. The reverse sorted digits are 710. The factorization of 710 is 2, 5, 71, therefore the 28th term in this sequence is 3.

Joshua Michael McAteer, Table of n, a(n) for n = 1..9592

Cf. A001222 (bigomega), A028906, A326952 (for ascending sorted version).

nmax= 100;
p = primes(nmax);
lp = length(p);
lfac = zeros(1, lp);
for i = 1:lp
digp=str2double(regexp(num2str(p(i)), '\d', 'match'));
ldigp = flip(sort(digp));
l=length(digp);
conv = 10.^flip(0:(l-1));
lnum = sum(conv.*ldigp);
lfac(i) = numel(factor(lnum));
end

A028911 Sort digits of primes into descending order (A028906) then sort this sequence into ascending order.

Original entry on oeis.org

2, 3, 5, 7, 11, 31, 31, 32, 41, 43, 53, 61, 71, 71, 73, 73, 74, 76, 83, 91, 92, 95, 97, 97, 98, 110, 211, 310, 311, 311, 311, 322, 331, 331, 332, 410, 421, 421, 431, 433, 443, 511, 521, 521, 530, 532, 533, 541, 610, 631, 631, 631, 632, 641, 641, 643, 643, 653

Offset: 0

N. J. A. Sloane

Take[Sort[FromDigits[Reverse[Sort[IntegerDigits[#]]]]&/@Prime[Range[200]]],60] (* Harvey P. Dale, Mar 26 2013 *)

More terms from Erich Friedman.

A028912 Sort digits of primes into descending order (A028906), sort this sequence into ascending order (A028911), then remove duplicates.

Original entry on oeis.org

2, 3, 5, 7, 11, 31, 32, 41, 43, 53, 61, 71, 73, 74, 76, 83, 91, 92, 95, 97, 98, 110, 211, 310, 311, 322, 331, 332, 410, 421, 431, 433, 443, 511, 521, 530, 532, 533, 541, 610, 631, 632, 641, 643, 653, 661, 710, 721, 722, 730, 731, 733, 743, 751, 752, 754, 755

Offset: 0

N. J. A. Sloane

Take[FromDigits[Reverse[Sort[IntegerDigits[#]]]]&/@Prime[Range[200]]//Union,60] (* Harvey P. Dale, Mar 31 2018 *)

More terms from Erich Friedman.

A069567 Smaller of two consecutive primes which are anagrams of each other.

Original entry on oeis.org

1913, 18379, 19013, 25013, 34613, 35617, 35879, 36979, 37379, 37813, 40013, 40213, 40639, 45613, 48091, 49279, 51613, 55313, 56179, 56713, 58613, 63079, 63179, 64091, 65479, 66413, 74779, 75913, 76213, 76579, 76679, 85313, 88379, 90379, 90679, 93113, 94379, 96079

Offset: 1

Amarnath Murthy, Mar 24 2002

Smaller members of Ormiston prime pairs.
Given the n-th prime, it is occasionally possible to form the (n+1)th prime using the same digits in a different order. Such a pair is called an Ormiston pair.
Ormiston pairs occur rarely but randomly. It is thought that there are infinitely many but this has not been proved. They always differ by a multiple of 18. Ormiston triples also exist - see A075093.
"Anagram" means that both primes must not only use the same digits but must use each digit the same number of times.  [From Harvey P. Dale, Mar 06 2012]
Dickson's conjecture would imply that the sequence is infinite, e.g. that there are infinitely many k for which 1913+3972900*k and 1931+3972900*k form an Ormiston pair. - Robert Israel, Feb 23 2017

			1913 and 1931 are two successive primes.
Although 179 and 197 are composed of the same digits, they do not form an Ormiston pair as several other primes intervene (i.e. 181, 191, 193).

Andy Edwards, Ormiston Pairs, Australian Mathematics Teacher, Vol. 58, No. 2 (2002), pp. 12-13.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Jens Kruse Andersen, Ormiston Tuples
Andy Edwards, Ormiston Pairs [Archive machine link]; local copy [with permission]
Eric Weisstein's World of Mathematics, Rearrangement Prime Pair.

Cf. A072274, A075093, A161160, A066540.

Cf. A000040, A028906.

import Data.List (sort)
a069567 n = a069567_list !! (n-1)
a069567_list = f a000040_list where
   f (p:ps@(p':_)) = if sort (show p) == sort (show p')
                     then p : f ps else f ps
-- Reinhard Zumkeller, Apr 03 2015

N:= 10^6: # to get all terms <= N
R:= NULL: p:= 3: q:= 5:
while p <= N do
  p:= q;
  q:= nextprime(q);
  if q-p mod 18 = 0 and sort(convert(p,base,10)) = sort(convert(q,base,10)) then
    R:= R, p
  fi
od:
R; # Robert Israel, Feb 23 2017

Prime[ Select[ Range[10^4], Sort[ IntegerDigits[ Prime[ # ]]] == Sort[ IntegerDigits[ Prime[ # + 1]]] & ]]
a = {1}; b = {2}; Do[b = Sort[ IntegerDigits[ Prime[n]]]; If[a == b, Print[ Prime[n - 1], ", ", Prime[n]]]; a = b, {n, 1, 10^4}]
Transpose[Select[Partition[Prime[Range[8600]],2,1],Sort[IntegerDigits[ First[#]]] == Sort[ IntegerDigits[Last[#]]]&]][[1]] (* Harvey P. Dale, Mar 06 2012 *)

is(n)=isprime(n)&&vecsort(Vec(Str(n)))==vecsort(Vec(Str(nextprime(n+1)))) \\ Charles R Greathouse IV, Aug 09 2011

p=2;forprime(q=3,1e5,if((q-p)%18==0&&vecsort(Vec(Str(p)))==vecsort(Vec(Str(q))),print1(p", "));p=q) \\ Charles R Greathouse IV, Aug 09 2011, minor edits by M. F. Hasler, Oct 11 2012

from sympy import nextprime
from itertools import islice
def agen(): # generator of terms
    p, hp, q, hq = 2, "2", 3, "3"
    while True:
        if hp == hq: yield p
        p, q = q, nextprime(q)
        hp, hq = hq, "".join(sorted(str(q)))
print(list(islice(agen(), 38))) # Michael S. Branicky, Feb 19 2024

Comments and references from Andy Edwards (AndynGen(AT)aol.com), Jul 09 2002
Edited by Robert G. Wilson v, Jul 15 2002 and Aug 29 2002
Minor edits by Ray Chandler, Jul 16 2009

A028905 Arrange digits of primes in ascending order.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 13, 37, 14, 34, 47, 35, 59, 16, 67, 17, 37, 79, 38, 89, 79, 11, 13, 17, 19, 113, 127, 113, 137, 139, 149, 115, 157, 136, 167, 137, 179, 118, 119, 139, 179, 199, 112, 223, 227, 229, 233, 239, 124, 125, 257, 236, 269

Offset: 1

N. J. A. Sloane

Leading zeros are discarded (e.g., 107, rearranged to 017, becomes 17).

			The digits of 41 are 4, 1, which sorted are 1, 4; those are reinterpreted as 14.
The digits of 43 are 4, 3, which sorted are 3, 4; those are reinterpreted as 34.
The digits of 47 are 4, 7, which are already sorted, so 47 is not changed.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A028906, A028864.

Cf. A004185, A000040.

a028905 = a004185 . a000040  -- Reinhard Zumkeller, Apr 03 2015

Table[FromDigits[Sort[IntegerDigits[Prime[n]]]], {n, 100}] (* Alonso del Arte, Nov 25 2019 *)

eva(n) = subst(Pol(n), x, 10)
a(n) = eva(vecsort(digits(prime(n)))) \\ Felix Fröhlich, Nov 25 2019

a(n) = A004185(A000040(n)). - Reinhard Zumkeller, Apr 03 2015

a(n) = prime(n) if prime(n) is in A028864. - Alonso del Arte, Nov 25 2019

More terms from Patrick De Geest, Apr 1998

Offset corrected by Reinhard Zumkeller, Apr 03 2015

cp's OEIS Frontend

A326953 a(n) = A001222(A028906(n)).

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A028911 Sort digits of primes into descending order (A028906) then sort this sequence into ascending order.

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A028912 Sort digits of primes into descending order (A028906), sort this sequence into ascending order (A028911), then remove duplicates.

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Author

Keywords

Programs

Mathematica

Extensions

A069567 Smaller of two consecutive primes which are anagrams of each other.

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A028905 Arrange digits of primes in ascending order.

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Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Mathematica

PARI

Formula

Extensions