A065582 Smallest prime ending in exactly n 9's.

19, 199, 1999, 49999, 199999, 2999999, 19999999, 799999999, 10999999999, 59999999999, 1099999999999, 34999999999999, 59999999999999, 499999999999999, 14999999999999999, 139999999999999999, 1099999999999999999, 20999999999999999999, 29999999999999999999, 2099999999999999999999

Offset: 1

Author

Robert G. Wilson v, Nov 28 2001

Keywords

• nonn
• base

Comments

From Jeppe Stig Nielsen, Jul 30 2022: (Start)

Can decrease, for example a(25) < a(24). So not the same as Smallest prime ending in n or more 9s.

a(n) can contain other 9s as well, for example a(46), a(118), a(156). (End)

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..500 (first 100 terms from Harry J. Smith).

Crossrefs

Cf. A037071, A065592, A065821, A065580, A065581.

Programs

Mathematica

Do[a = Table[9, {n} ]; k = 0; While[ b = FromDigits[ Join[ IntegerDigits[k], a]]; Mod[k, 10] == 9 || !PrimeQ[b], k++ ]; Print[b], {n, 1, 17} ]

PARI

a(n)={ my(t=10^n, b=t-1, d=0); while(!isprime(b + t*d), d++; if(d%10==9, d++)); b + t*d } \\ Harry J. Smith, Oct 23 2009

Python

from sympy import isprime
def a(n):
    pow, end, i = 10**n, 10**n-1, 1
    while i%10 == 9 or not isprime(i*pow + end): i += 1
    return i*pow + end
print([a(n) for n in range(1, 20)]) # Michael S. Branicky, Jul 30 2022