A276707 Number of terms of A069090 with exactly n digits.

4, 12, 60, 381, 2522, 19094, 151286, 1237792, 10354144, 88407746, 766869330

Offset: 1

Author

Barry Carter, Sep 15 2016

Keywords

• nonn
• base
• more

Links

• Barry Carter, Mathematica work on first n for which randomly rolled digits will yield a prime

Crossrefs

Cf. A069090.

Programs

Maple

A276707 := proc(n)
    local a,k;
    a := 0 ;
    k := nextprime(10^(n-1)) ;
    while k < 10^n do
        if isA069090(k) then
            a := a+1 ;
        end if;
        k := nextprime(k) ;
    end do:
    a ;
end proc: # R. J. Mathar, Dec 15 2016

Python

from sympy import primerange, isprime
def ok(p):
    s = str(p)
    if len(s) == 1: return True
    return all(not isprime(int(s[:i])) for i in range(1, len(s)))
def a(n): return sum(ok(p) for p in primerange(10**(n-1), 10**n))
print([a(n) for n in range(1, 7)]) # Michael S. Branicky, Jul 03 2021

Python

# faster version skipping bad prefixes
from sympy import isprime, nextprime
def a(n):
    if n == 1: return 4
    p, c = nextprime(10**(n-1)), 0
    while p < 10**n:
        s, fail = str(p), False
        for i in range(1, n):
            ti = int(s[:i])
            if isprime(ti): fail = i; break
        if fail: p = nextprime((ti+1)*10**(n-i))
        else: p, c = nextprime(p), c+1
    return c
print([a(n) for n in range(1, 8)]) # Michael S. Branicky, Jul 03 2021

Extensions

a(9)-a(11) from Michael S. Branicky, Jul 03 2021