A052014 -id:A052014 - cp's OEIS frontend

A028864 Primes with digits in nondecreasing order.

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

A052015 Primes with distinct digits in ascending order.

Original entry on oeis.org

2, 3, 5, 7, 13, 17, 19, 23, 29, 37, 47, 59, 67, 79, 89, 127, 137, 139, 149, 157, 167, 179, 239, 257, 269, 347, 349, 359, 367, 379, 389, 457, 467, 479, 569, 1237, 1249, 1259, 1279, 1289, 1367, 1459, 1489, 1567, 1579, 1789, 2347, 2357, 2389, 2459, 2467, 2579

Offset: 1

Patrick De Geest, Nov 15 1999

			Last term is a(100) = 23456789.

T. D. Noe, Table of n, a(n) for n = 1..100 (complete sequence)

Cf. A028864, A028867, A052014.

b:= proc(n) `if`(isprime(n), n, [][]), seq(
      b(parse(cat(n, j))), j=irem(n, 10)+1..9)
    end:
sort([seq(b(n), n=1..9)])[];  # Alois P. Heinz, Jun 16 2025

t={};Do[p=Prime[n];If[Select[Differences[IntegerDigits[p]],#<=0&]=={},AppendTo[t,p]],{n,380}];t (* Jayanta Basu, May 04 2013 *)
Select[Prime[Range[5000]],Min[Differences[IntegerDigits[#]]]>0&] (* Harvey P. Dale, Jun 20 2015 *)
Select[FromDigits@# &/@Subsets@Range@9,PrimeQ] (* Hans Rudolf Widmer, Apr 08 2023 *)

A052015=vecextract( vecsort( vector( 511,i,isprime( t=eval( concat( vecextract(Vec("123456789"),i ))))*t),NULL,8),"^1") /* for old PARI versions replace,NULL,8),"^1" by ),"-100.." */ \\ M. F. Hasler, Jan 27 2009

from sympy import isprime
from itertools import combinations
def agen(): # generator of terms
    for d in range(1, 9):
        for c in combinations("123456789", d):
            if isprime(t:=int("".join(c))):
                yield t
print(list(agen())) # Michael S. Branicky, Dec 13 2023

A028867 Primes with digits in nonincreasing order.

Original entry on oeis.org

2, 3, 5, 7, 11, 31, 41, 43, 53, 61, 71, 73, 83, 97, 211, 311, 331, 421, 431, 433, 443, 521, 541, 631, 641, 643, 653, 661, 733, 743, 751, 761, 773, 811, 821, 853, 863, 877, 881, 883, 887, 911, 941, 953, 971, 977, 983, 991, 997, 2111, 2221, 3221

Offset: 1

Patrick De Geest

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

Cf. A052014, A028864, A052015.

t={};Do[p=Prime[n];If[Select[Differences[IntegerDigits[p]],#>0&]=={},AppendTo[t,p]],{n,460}];t (* Jayanta Basu, May 04 2013 *)
Select[Prime[Range[600]],Max[Differences[IntegerDigits[#]]]<1&] (* Harvey P. Dale, Oct 30 2013 *)

is(n)=my(d=digits(n)); for(i=2,#d,if(d[i]>d[i-1],return(0))); isprime(n) \\ Charles R Greathouse IV, Aug 18 2017

from itertools import count, islice, combinations_with_replacement
from sympy import isprime
def A028867_gen(): # generator of terms
    yield from (2,3,5,7)
    a, b = {'1':1,'2':1,'3':2,'4':2,'5':2,'6':2,'7':3,'8':3,'9':4}, (1,3,7,9)
    for l in count(1):
        mlist = []
        for d in combinations_with_replacement('987654321',l):
            k = 10*int(''.join(d))
            for e in b[:a[d[-1]]]:
                if isprime(m:=k+e):
                    mlist.append(m)
        yield from sorted(mlist)
A028867_list = list(islice(A028867_gen(),30)) # Chai Wah Wu, Dec 25 2023

Definition corrected by Omar E. Pol, Mar 22 2012

A190219 Numbers all of whose divisors have decimal digits in strictly decreasing order.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 21, 31, 40, 41, 43, 53, 61, 62, 63, 71, 73, 82, 83, 86, 93, 97, 421, 431, 521, 541, 631, 641, 643, 653, 743, 751, 761, 821, 842, 853, 862, 863, 941, 953, 961, 971, 983, 5431, 6421, 6521, 7321, 7541, 7621, 7643, 8431, 8521

Offset: 1

Jaroslav Krizek, May 06 2011

Sequence is finite. Last term a(104) = 98765431.

Subset of A009995 and A190220. Superset of A052014.

			Number 93 is in sequence because all divisors of 93 (1, 3, 31, 93) are numbers whose decimal digits are in strictly decreasing order.

Nathaniel Johnston, Table of n, a(n) for n = 1..104 (full sequence)

with(numtheory): A190219 := proc(n) option remember: local d,dd,i,j,k,m,poten: if(n=1)then return 1: fi: for k from procname(n-1)+1 do d:=divisors(k): poten:=1: for i from 1 to nops(d) do m:=-1: dd:=convert(d[i],base,10): for j from 1 to nops(dd) do if(mA190219(n),n=1..60); # Nathaniel Johnston, May 06 2011

Select[Range[9000],Max[Flatten[Differences/@(IntegerDigits/@Divisors[#])]]<0&] (* Harvey P. Dale, Feb 22 2024 *)

A061245 Prime numbers with odd digits in descending order.

Original entry on oeis.org

3, 5, 7, 11, 31, 53, 71, 73, 97, 311, 331, 733, 751, 773, 911, 953, 971, 977, 991, 997, 3331, 5333, 5531, 7331, 7333, 7753, 9311, 9511, 9533, 9551, 9733, 9931, 9973, 33311, 33331, 55331, 55333, 55511, 73331, 75511, 75533, 75553, 77551, 77711

Offset: 1

Amarnath Murthy, Apr 23 2001

Cf. A061244, A028867, A052014.

More terms from Patrick De Geest, Jun 04 2001

A212372 Nonprime numbers with distinct digits in descending order.

Original entry on oeis.org

1, 4, 6, 8, 9, 10, 20, 21, 30, 32, 40, 42, 50, 51, 52, 54, 60, 62, 63, 64, 65, 70, 72, 74, 75, 76, 80, 81, 82, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 96, 98, 210, 310, 320, 321, 410, 420, 430, 432, 510, 520, 530, 531, 532, 540, 542, 543, 610, 620, 621, 630

Offset: 1

Jaroslav Krizek, May 10 2012

Sequence is finite with 935 terms, last term is a(935) = 9876543210.

Complement of A052014 with respect to A009995.

Jaroslav Krizek, Table of n, a(n) for n = 1..935 (complete list).

Cf. A052014 (primes with distinct digits in descending order), A009995 (numbers with distinct digits in descending order).

A178788(a(n)) = 1.

A381158 Prime numbers where digit values decrease while alternating parity.

Original entry on oeis.org

2, 3, 5, 7, 41, 43, 61, 83, 521, 541, 743, 761, 941, 983, 6521, 8521, 8543, 8741, 8761, 76541, 76543, 94321, 98321, 98543

Offset: 1

James S. DeArmon, Feb 15 2025

			41 is a term, since the digits decrease in value and alternate even and odd.

Cf. A052014, A000040, A028867, A028864, A052015, A382027.

b:= proc(n) `if`(isprime(n), n, [][]), seq(b(10*n+j), j=irem(n, 10)-1..1, -2) end:
{seq(b(n), n=1..9)}[];  # Alois P. Heinz, Mar 12 2025

ad=Select[Prime[Range[10^6]],Reverse[Union[IntegerDigits[#]]]==IntegerDigits[#]&];fQ[n_] := Block[{m = Mod[ IntegerDigits@ n, 2]}, m == Split[m, UnsameQ][[1]]];Select[ad,fQ] (* James C. McMahon, Mar 20 2025 *)

from sympy import isprime
from itertools import combinations
def ap(s): return all((s[i] in "13579") == (s[i+1] in "02468") for i in range(len(s)-1))
def afull(): return sorted(t for d in range(1, 10) for c in combinations("987654321", d) if ap(c) and isprime(t:=int("".join(c))))
print(afull()) # Michael S. Branicky, Mar 10 2025

A155768 Indices of primes with digits in strictly decreasing order.

Original entry on oeis.org

1, 2, 3, 4, 11, 13, 14, 16, 18, 20, 21, 23, 25, 82, 83, 98, 100, 115, 116, 117, 119, 132, 133, 135, 142, 147, 150, 160, 162, 164, 166, 717, 835, 843, 933, 956, 968, 970, 1055, 1062, 1066, 1076, 1088, 1090, 1092, 1093, 1166, 1167, 1179, 1190, 1191, 1199, 1202

Offset: 1

Zak Seidov, Jan 27 2009

Indices of primes in A052014.

There are exactly 87 terms: 1,2,3,4,11,13,14,16,18,20,21,23,25,82,83,98,100,115,116,117,119,132,133,135,142,147,150,160,162,164,166,717,835,843,933,956,968,970,1055,1062,1066,1076,1088,1090,1092,1093,1166,1167,1179,1190,1191,1199,1202,1215,1218,7433,7518,7530,7531,8414,8486,8498,8509,8510,8511,9096,9286,9391,9441,9463,9468,9471,9479,61307,68743,69564,76755,77533,77608,77614,587773,587837,649440,656917,5634190,5694444,5694505

A052014.

Select[Range[1300],And@@Negative[Differences[IntegerDigits[Prime[#]]]]&] (* Harvey P. Dale, Nov 24 2011 *)

A261511 Twin primes with both terms having distinct digits in descending order.

Original entry on oeis.org

3, 5, 7, 41, 43, 71, 73, 641, 643, 76541, 76543, 87641, 87643

Offset: 1

Paolo Omodei-Zorini, Aug 22 2015

Numbers in this list are the pairs of twin primes listed in A052014 with both terms having distinct digits in descending order

Cf. A001097, A052014.

dsc[n_] := 0 > Max@ Differences@ IntegerDigits@n; Union@ Flatten@ Select[ Partition[ Prime@ Range@ 9000, 2, 1], #[[2]] - #[[1]] == 2 && And @@ dsc /@ # &] (* Giovanni Resta, Aug 26 2015 *)

lista(nn=100000) = {v = []; forprime(p=2, nn, if (isprime(p+2) && (d=digits(p)) && (vecsort(d,,12)==d) && (dd=digits(p+2)) && (vecsort(dd,,12)==dd), v = concat(v, p); v = concat(v,p+2));); vecsort(v,,8);} \\ Michel Marcus, Aug 23 2015

cp's OEIS Frontend

A028864 Primes with digits in nondecreasing order.

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A052015 Primes with distinct digits in ascending order.

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A028867 Primes with digits in nonincreasing order.

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A190219 Numbers all of whose divisors have decimal digits in strictly decreasing order.

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A061245 Prime numbers with odd digits in descending order.

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A212372 Nonprime numbers with distinct digits in descending order.

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A381158 Prime numbers where digit values decrease while alternating parity.

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A155768 Indices of primes with digits in strictly decreasing order.

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