A186142 a(n) is the smallest suffix such that the numbers with k digits "9" prepended are primes for k = 1, 2, ..., n.

7, 7, 29, 907, 32207, 573217, 3136717, 4128253, 2181953771, 2181953771, 2181953771

Offset

1,1

Comments

See A186143 for the digit "3" case. The corresponding sequences with the digits "1" or "7" are not possible because if Xn and XXn are prime, then XXXn will be a multiple of 3 when X is 1 or 7.

By construction, a(n+1) >= a(n). - Michael S. Branicky, Jul 07 2021

From Bernard Schott, Dec 20 2021: (Start)

If the restriction "but not for k = n+1" is added, the terms become 11, 7, 29, 907, 32207, 573217, 3136717, ... In this case, the 1st term becomes 11 because 911 is prime while 9911 is divisible by 11.

In complement of 1st comment, the corresponding sequences with the digits "2", "4", "5" or "8" are not also possible for the same reasons. See A350216 for the digit "6" case. (End)

Links

Table of n, a(n) for n=1..11.

Example

a(3) = 29 because 929, 9929, 99929 are primes.

Mathematica

m=1; Table[While[d=IntegerDigits[m]; k=0; While[k++; PrependTo[d, 9]; k <= n && PrimeQ[FromDigits[d]]]; k <= n, m++]; m, {n, 6}]

Prog

(Python)
from sympy import isprime
def a(n, startfrom=1):
  an = startfrom + (1 - startfrom%2)
  while not all(isprime(int("9"*k+str(an))) for k in range(1, n+1)): an+=2
  return an
def afind(nn):
  an = 1
  for n in range(1, nn+1): an = a(n, startfrom=an); print(an, end=", ")
afind(8) # Michael S. Branicky, Jul 07 2021

Crossrefs

Cf. A186069, A186070, A186143, A350214, A350216.

Sequence in context: A299338 A341246 A246039 * A188274 A255281 A255283

Adjacent sequences: A186139 A186140 A186141 * A186143 A186144 A186145

Keyword

nonn,base

Author

Michel Lagneau, Feb 13 2011

Extensions

a(9)-a(11) from Michael S. Branicky, Jul 07 2021

Status

approved