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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.

%I A350246 #25 Jan 14 2022 11:24:24
%S A350246 11,3,18,15,42,189,306,369,6,1176,93,963,2202,750,408,498,267,1875,
%T A350246 240,2751,798,1929,3402,6162,6195,4953,5004,8130,18591,20019,4461,
%U A350246 1851,46866,29232,7206,24807,4644,23307,48528,21594,28236,4353,28212,3003,22611,50760
%N 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.
%C A350246 First observed by J. A. Hervás Contreras (see the links).
%C A350246 Every term (from the second on) is a multiple of 3.
%H A350246 Chai Wah Wu, <a href="/A350246/b350246.txt">Table of n, a(n) for n = 1..100</a>
%H A350246 José Antonio Hervás Contreras, <a href="https://www.gaussianos.com/forogauss/topic/nueva-propiedad-de-los-primos-gemelos/">¿Nueva propiedad de los primos gemelos?</a>
%e A350246 11, 311, 18311, 1518311, and 421518311 are terms of A001359.
%p A350246 terms := proc(n)
%p A350246    local i, j, p, q, L, M:
%p A350246    i, L, M := 0, [11], [11]:
%p A350246    while numelems(L) < n do
%p A350246       i, j := i+1, 0:
%p A350246       while 1 > 0 do
%p A350246          j, p := j+1, M[numelems(M)]:
%p A350246          q := parse(cat(j, p)):
%p A350246          if isprime(q) and isprime(q+2) then
%p A350246             L, M := [op(L), j], [op(M), q]:
%p A350246             break: fi: od: od:
%p A350246    L: end:
%o A350246 (Python)
%o A350246 from itertools import count, islice
%o A350246 from sympy import isprime
%o A350246 def A350246_gen(): # generator of terms
%o A350246     yield 11
%o A350246     s = '11'
%o A350246     while True:
%o A350246         for k in count(3,3):
%o A350246             t = str(k)
%o A350246             m = int(t+s)
%o A350246             if isprime(m) and isprime(m+2):
%o A350246                 yield k
%o A350246                 break
%o A350246         s = t+s
%o A350246 A350246_list = list(islice(A350246_gen(),20)) # _Chai Wah Wu_, Jan 12 2022
%Y A350246 Cf. A001359.
%K A350246 nonn,base
%O A350246 1,1
%A A350246 _Lorenzo Sauras Altuzarra_, Dec 21 2021