A345325 Number of primes less than 10^n with digits in nondecreasing order.

0, 4, 16, 50, 132, 315, 689, 1413, 2636, 4967, 8563, 14481, 23593, 37127, 56809, 86779, 127096, 184517, 264288, 368794, 510442, 707483, 948307, 1268871, 1689642, 2204795, 2866855, 3729223, 4738019, 6013021, 7619227, 9510372, 11832748, 14770667, 18067652

Offset

0,2

Comments

Number of primes with at most n digits arranged in nondecreasing 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@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("123456789", 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, A028864, A345326.

Sequence in context: A217950 A217949 A227675 * A203094 A298173 A323932

Adjacent sequences: A345322 A345323 A345324 * A345326 A345327 A345328

Keyword

nonn,base,hard

Author

Ilya Gutkovskiy, Jul 22 2021

Extensions

a(11)-a(34) from Michael S. Branicky, Jul 22 2021

Status

approved