A345326 Number of primes less than 10^n with digits in nonincreasing order.

0, 4, 14, 49, 125, 296, 646, 1304, 2459, 4543, 7882, 13272, 21856, 34934, 53446, 82055, 121322, 175498, 251714, 354810, 488440, 676065, 914834, 1220629, 1627770, 2135954, 2759889, 3590609, 4602572, 5830588, 7386200, 9266652, 11469407, 14314939, 17658240

Offset: 0

Author

Ilya Gutkovskiy, Jul 22 2021

Keywords

• nonn
• base
• hard

Comments

Number of primes with at most n digits arranged in nonincreasing order.

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..42
• Index entries for sequences related to numbers of primes in various ranges

Crossrefs

Cf. A000040, A006880, A028867, A345325.

Programs

Mathematica

Table[Length@Select[Prime@Range[PrimePi[10^n]],OrderedQ@Reverse@IntegerDigits@#&],{n,0,7}] (* Giorgos Kalogeropoulos, Jul 22 2021 *)

Python

from sympy import isprime
from itertools import accumulate, combinations_with_replacement as mc
def numwithdigs(d):
    if d == 0: return 0
    nonincreasing = (int("".join(m)) for m in mc("987654321", d))
    return len(list(filter(isprime, nonincreasing)))
def aupto(nn): return list(accumulate(numwithdigs(d) for d in range(nn+1)))
print(aupto(14)) # Michael S. Branicky, Jul 22 2021

Extensions

a(12)-a(34) from Michael S. Branicky, Jul 22 2021