A028867 Primes with digits in nonincreasing order.

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

Author

Patrick De Geest

Keywords

• nonn
• base

Links

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

Crossrefs

Cf. A052014, A028864, A052015.

Programs

Mathematica

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 *)

PARI

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

Python

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

Extensions

Definition corrected by Omar E. Pol, Mar 22 2012