A028905 -id:A028905 - cp's OEIS frontend

A326952 a(n) = A001222(A028905(n)).

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

Offset: 1

Joshua Michael McAteer, Aug 06 2019

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

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

			The 13th prime number is 41. Sorting the digits gives 14. 14 has 2 factors, 2 and 7. The 13th term of this sequence is 2.

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

Cf. A001222 (bigomega), A028905, A326953 (for reverse sorting).

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

A028864 Primes with digits in nondecreasing order.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 47, 59, 67, 79, 89, 113, 127, 137, 139, 149, 157, 167, 179, 199, 223, 227, 229, 233, 239, 257, 269, 277, 337, 347, 349, 359, 367, 379, 389, 449, 457, 467, 479, 499, 557, 569, 577, 599, 677, 1117, 1123, 1129

Offset: 1

Patrick De Geest

Identical digits are acceptable, e.g., 1117 is in the sequence. - Harvey P. Dale, Aug 16 2011

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (terms n = 1..1000 from T. D. Noe)

Cf. A009994, A052015, A028867, A052014, A028905.

[p:p in PrimesUpTo(1200)| Reverse(Intseq(p)) eq Sort(Intseq(p))]; // Marius A. Burtea, Nov 29 2019

daoQ[n_] := Count[Differences[IntegerDigits[n]], ?(# < 0 &)] == 0; Select[Prime[Range[200]], daoQ] (* _Harvey P. Dale, Aug 16 2011 *)
Select[Prime[Range[200]],Min[Differences[IntegerDigits[#]]]>-1&] (* Harvey P. Dale, Mar 02 2023 *)

select(n->n=digits(n); n==vecsort(n), primes(500)) \\ Charles R Greathouse IV, Mar 15 2014

from itertools import count, islice, combinations_with_replacement
from sympy import isprime
def A028864_gen(): # generator of terms
    yield from (2,3,5,7)
    a, b = {'1':0,'2':1,'3':1,'4':2,'5':2,'6':2,'7':2,'8':3,'9':3}, (1,3,7,9)
    for l in count(1):
        for d in combinations_with_replacement('123456789',l):
            k = 10*int(''.join(d))
            for e in b[a[d[-1]]:]:
                if isprime(m:=k+e):
                    yield m
A028864_list = list(islice(A028864_gen(),30)) # Chai Wah Wu, Dec 25 2023

j=2; y=as.bigz(c()); while(j<1000) {
x=sort(as.numeric(strsplit(as.character(j),spl="")[[1]]),decr=F)
if(j==paste(x[x>0],collapse="")) y=c(y,j)
j=nextprime(j)
} //  Christian N. K. Anderson, Apr 04 2013

Trivially, a(n) >> exp(n^(1/10)). - Charles R Greathouse IV, Mar 15 2014

prime(n) = A028905(n) if prime(n) is in this sequence. - Alonso del Arte, Nov 25 2019

Definition corrected by Omar E. Pol, Mar 22 2012

A028906 Arrange digits of primes in descending order.

Original entry on oeis.org

2, 3, 5, 7, 11, 31, 71, 91, 32, 92, 31, 73, 41, 43, 74, 53, 95, 61, 76, 71, 73, 97, 83, 98, 97, 110, 310, 710, 910, 311, 721, 311, 731, 931, 941, 511, 751, 631, 761, 731, 971, 811, 911, 931, 971, 991, 211, 322, 722, 922, 332, 932, 421, 521

Offset: 1

N. J. A. Sloane

a(n) = A004186(A000040(n)). - Reinhard Zumkeller, Apr 03 2015

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

Cf. A028905.

Cf. A004186, A000040.

a028906 = a004186 . a000040  -- Reinhard Zumkeller, Apr 03 2015

Table[FromDigits[Reverse[Sort[IntegerDigits[Prime[n]]]]],{n,60}] (* Harvey P. Dale, Sep 12 2020 *)

More terms from Patrick De Geest, Apr 15 1998

cp's OEIS Frontend

A326952 a(n) = A001222(A028905(n)).

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A028864 Primes with digits in nondecreasing order.

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A028906 Arrange digits of primes in descending order.

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