A068120 -id:A068120 - cp's OEIS frontend

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

Amarnath Murthy, Oct 27 2003

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

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

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

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 */

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

More terms from Ray Chandler, Nov 01 2003

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

A068008 Least number needed to be appended to n n's to make a prime that does not contain more than n n's in a row.

Original entry on oeis.org

2, 3, 3, 1, 9, 7, 29, 39, 3, 43, 39, 1, 23, 27, 97, 53, 91, 37, 251, 93, 93, 19, 97, 61, 293, 153, 163, 1, 297, 103, 323, 61, 127, 113, 31, 127, 353, 67, 841, 187, 9, 21, 179, 429, 127, 97, 3, 319, 11, 51, 39, 191, 33, 3, 41, 151, 39, 47, 169, 787, 401, 57, 441, 571

Offset: 0

Robert G. Wilson v, Feb 22 2002

This is not quite the "tail" of the numbers in A068120 because of the restriction that a(n) cannot begin with a zero. For example, a(25) = 153; 25252525252525252525252525252525252525252525252525153 is a prime, but it is greater than A068120(25) = 25252525252525252525252525252525252525252525252525061. - Dan Dima, Jan 29 2007

			a(0) = 2 because appending 2 to a zero-length string (i.e., 0 0's) yields 2, which is prime.
a(1) = 3 because appending a 3 to 1 yields 13, which is prime; a(1) is not 1, because appending a 1 to 1 yields 11, which (although prime) contains more than one 1 in a row.
a(2) = 3 because appending a 3 to 22 yields 223 (prime), whereas appending a 1 produces the nonprime 221=13*17.

Cf. A068120.

Examples edited, and definition edited to match the rationale for a(1)=3 (not 1), by Jon E. Schoenfield, Sep 21 2013

cp's OEIS Frontend

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

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