A342221 Integers k, not congruent to 1 mod 3, such that there is no prime of length k using digit 3 once and rest all 1.

15, 26, 32, 41, 68, 93, 99, 113, 116, 119, 134, 150, 158, 161, 170, 173, 176, 177, 179, 204, 213, 252, 257, 266, 284, 299, 305, 312, 320, 333, 353, 357, 374, 392, 402, 404, 419, 434, 443, 450, 491, 495, 506, 509, 513, 518, 527, 548, 551, 554, 570, 582, 584, 593

Offset

1,1

Comments

The "not congruent to 1 mod 3" condition is due to the fact that A090537(3*k+1) = 0.

Links

Table of n, a(n) for n=1..54.

Prog

(Python)
from sympy import isprime
A342221_list = []
for k in range(1, 10**3):
    if k % 3 != 1:
        m, l = (10**k-1)//9, 2
        for i in range(k):
            if isprime(m+l):
                break
            l *= 10
        else:
            A342221_list.append(k) # Chai Wah Wu, Mar 15 2021

Crossrefs

Cf. A090537, A107689.

Subsequence of A007494.

Sequence in context: A146249 A248834 A249109 * A074974 A191913 A191915

Adjacent sequences: A342218 A342219 A342220 * A342222 A342223 A342224

Keyword

nonn,base

Author

Michel Marcus, Mar 14 2021

Extensions

More terms from Chai Wah Wu, Mar 15 2021

Status

approved