A350246 - OEIS

%I #25 Jan 14 2022 11:24:24

%S 11,3,18,15,42,189,306,369,6,1176,93,963,2202,750,408,498,267,1875,

%T 240,2751,798,1929,3402,6162,6195,4953,5004,8130,18591,20019,4461,

%U 1851,46866,29232,7206,24807,4644,23307,48528,21594,28236,4353,28212,3003,22611,50760

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

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

%H Chai Wah Wu, <a href="/A350246/b350246.txt">Table of n, a(n) for n = 1..100</a>

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

%p terms := proc(n)

%p    local i, j, p, q, L, M:

%p    i, L, M := 0, [11], [11]:

%p    while numelems(L) < n do

%p       i, j := i+1, 0:

%p       while 1 > 0 do

%p          j, p := j+1, M[numelems(M)]:

%p          q := parse(cat(j, p)):

%p          if isprime(q) and isprime(q+2) then

%p             L, M := [op(L), j], [op(M), q]:

%p             break: fi: od: od:

%p    L: end:

%o (Python)

%o from itertools import count, islice

%o from sympy import isprime

%o def A350246_gen(): # generator of terms

%o     yield 11

%o     s = '11'

%o     while True:

%o         for k in count(3,3):

%o             t = str(k)

%o             m = int(t+s)

%o             if isprime(m) and isprime(m+2):

%o                 yield k

%o                 break

%o         s = t+s

%o A350246_list = list(islice(A350246_gen(),20)) # _Chai Wah Wu_, Jan 12 2022

%Y Cf. A001359.

%K nonn,base

%O 1,1

%A _Lorenzo Sauras Altuzarra_, Dec 21 2021