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

0,2

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000040, A006880, A028867, A345325.

Sequence in context: A111299 A245824 A356121 * A327610 A110686 A071729

Adjacent sequences: A345323 A345324 A345325 * A345327 A345328 A345329

Keyword

nonn,base,hard

Author

Ilya Gutkovskiy, Jul 22 2021

Extensions

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

Status

approved