A088639 Smallest prime beginning with at least n n's (in decimal notation).

2, 11, 223, 3331, 44449, 555557, 66666629, 777777701, 888888883, 99999999907, 1010101010101010101039, 11111111111111111111111, 12121212121212121212121223, 1313131313131313131313131301, 141414141414141414141414141497, 15151515151515151515151515151501

Offset: 0

Author

Amarnath Murthy, Oct 27 2003

Keywords

• base
• easy
• nonn

Links

• M. F. Hasler, Table of n, a(n) for n=0..100

Crossrefs

Cf. A088640. See A068120 for another version. See also A065584 - A065592.

Programs

Maple

a:= proc(n) local d, h, s;
      s:= parse(cat(0, n$n));
      for d from 0 do
        for h to 10^d-1 do
          if isprime(s+h) then return s+h fi
        od:
        s:= s*10;
      od
    end:
seq(a(n), n=0..16);  # Alois P. Heinz, Feb 11 2021

PARI

A088639(n)={ local(p=10^#Str(n),d=1); n*=(p^n-1)/(p-1); until( (d*=10)*(n+1)>p=nextprime(n*d), );p} /* M. F. Hasler, Jan 13 2009 */

Python

from sympy import isprime
def a(n):
  if n == 0: return 2
  nns, i, pow10 = int(str(n)*n), 1, 1
  while True:
    i = 1
    while i < pow10:
      t = nns * pow10 + i
      if isprime(t): return t
      i += 2
    pow10 *= 10
print([a(n) for n in range(16)]) # Michael S. Branicky, Feb 11 2021

Extensions

More terms from Ray Chandler, Nov 01 2003

More cross-references and initial term added by M. F. Hasler, Jan 13 2009