A350246 a(n) is the minimum positive integer k such that the concatenation of k, a(n-1), a(n-2), ..., a(2), and a(1) is the lesser of a pair of twin primes (i.e., a term of A001359), with a(1) = 11.

11, 3, 18, 15, 42, 189, 306, 369, 6, 1176, 93, 963, 2202, 750, 408, 498, 267, 1875, 240, 2751, 798, 1929, 3402, 6162, 6195, 4953, 5004, 8130, 18591, 20019, 4461, 1851, 46866, 29232, 7206, 24807, 4644, 23307, 48528, 21594, 28236, 4353, 28212, 3003, 22611, 50760

Offset: 1

Author

Lorenzo Sauras Altuzarra, Dec 21 2021

Keywords

• nonn
• base

Comments

First observed by J. A. Hervás Contreras (see the links).

Every term (from the second on) is a multiple of 3.

Examples

			11, 311, 18311, 1518311, and 421518311 are terms of A001359.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..100
• José Antonio Hervás Contreras, ¿Nueva propiedad de los primos gemelos?

Crossrefs

Cf. A001359.

Programs

Maple

terms := proc(n)
   local i, j, p, q, L, M:
   i, L, M := 0, [11], [11]:
   while numelems(L) < n do
      i, j := i+1, 0:
      while 1 > 0 do
         j, p := j+1, M[numelems(M)]:
         q := parse(cat(j, p)):
         if isprime(q) and isprime(q+2) then
            L, M := [op(L), j], [op(M), q]:
            break: fi: od: od:
   L: end:

Python

from itertools import count, islice
from sympy import isprime
def A350246_gen(): # generator of terms
    yield 11
    s = '11'
    while True:
        for k in count(3,3):
            t = str(k)
            m = int(t+s)
            if isprime(m) and isprime(m+2):
                yield k
                break
        s = t+s
A350246_list = list(islice(A350246_gen(),20)) # Chai Wah Wu, Jan 12 2022