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

Author

Michel Marcus, Mar 14 2021

Keywords

• nonn
• base

Comments

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

Crossrefs

Cf. A090537, A107689.

Subsequence of A007494.

Programs

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

Extensions

More terms from Chai Wah Wu, Mar 15 2021