A186143 a(n) is the smallest suffix such that the numbers with k digits "3" prepended are primes for k = 1, 2, ..., n.

1, 1, 1, 1, 1, 1, 1, 26009371, 1233803717, 24680858269

Offset

1,8

Comments

See A186142 for the digit "9" 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.

A350214 is a variant where the first six terms are not equal to 1. - Bernard Schott, Mar 10 2022

Links

Table of n, a(n) for n=1..10.

Example

a(7) = 1 because 31, 331, 3331, 33331, 333331, 3333331, 33333331 are primes.

Mathematica

m=1; Table[While[d=IntegerDigits[m]; k=0; While[k++; PrependTo[d, 3]; k <=
  n && PrimeQ[FromDigits[d]]]; k <= n, m++]; m, {n, 6}]

Prog

(Python)
from sympy import isprime
def a(n):
    an = 0
    while True:
        an = an+1
        while not all(isprime(int("3"*k+str(an))) for k in range(1, n+1)):
            an += 1
        return an
print([a(n) for n in range(1, 9)]) # Michael S. Branicky, Mar 10 2022

Crossrefs

Cf. A186142, A186069, A186070, A350214.

Sequence in context: A340582 A234358 A113026 * A216005 A120410 A246225

Adjacent sequences: A186140 A186141 A186142 * A186144 A186145 A186146

Keyword

nonn,base,hard,more

Author

Michel Lagneau, Feb 13 2011

Extensions

a(9)-a(10) from Jonathan Pappas, Oct 22 2021

Status

approved