A374233 Irregular triangle read by rows where row n lists the primes containing at least one digit not seen in any smaller prime in base n, for n >= 2.

2, 2, 3, 2, 3, 5, 17, 2, 3, 5, 19, 2, 3, 5, 7, 29, 37, 2, 3, 5, 7, 11, 13, 2, 3, 5, 7, 11, 37, 53, 67, 2, 3, 5, 7, 11, 13, 17, 59, 83, 2, 3, 5, 7, 11, 19, 41, 61, 83, 101, 2, 3, 5, 7, 11, 17, 19, 31, 37, 43, 2, 3, 5, 7, 11, 13, 53, 73, 97, 109, 127, 149

Offset: 2

Author

Nicolas Bělohoubek, Jul 01 2024

Keywords

• base
• easy
• nonn
• tabf

Examples

			Row n=4 is 2, 3, 5, 17, which is 2_4, 3_4, 11_4, 101_4.
First few rows:
       k=1  2  3   4   5   6   7   8
  n=2:  [2],
  n=3:  [2, 3],
  n=4:  [2, 3, 5, 17],
  n=5:  [2, 3, 5, 19],
  n=6:  [2, 3, 5,  7, 29, 37],
  n=7:  [2, 3, 5,  7, 11, 13],
  n=8:  [2, 3, 5,  7, 11, 37, 53, 67],
  ...
		

Crossrefs

Cf. A033274.

Programs

PARI

isok(d, digs) = for (i=1, #d, if (!vecsearch(digs, d[i]), return(1)));
row(n) = my(digs=List(), v=List()); forprime(p=2, , my(d = digits(p, n)); if (isok(d, Vec(digs)), listput(v, p); for (i=1, #d, listput(digs, d[i])); listsort(digs, 1); if (#digs == n, return(Vec(v))););); \\ Michel Marcus, Jul 02 2024

Python

from sympy.ntheory import digits, nextprime
def row(n):
    if n == 2: return [2]
    p, r, used = 2, [2], {2}
    while len(used) < n:
        while (ds:=set(digits(p:=nextprime(p), n)[1:])) <= used: pass
        r.append(p)
        used |= ds
    return r
print([an for b in range(2, 13) for an in row(b)]) # Michael S. Branicky, Jul 01 2024